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Decompositions of Dynamical Systems Induced by the Koopman Operator Anal. Math. (IF 0.527) Pub Date : 2021-01-16 K. Küster
For a topological dynamical system we characterize the decomposition of the state space induced by the fixed space of the corresponding Koopman operator. For this purpose, we introduce a hierarchy of generalized orbits and obtain the finest decomposition of the state space into absolutely Lyapunov stable sets. Analogously to the measure-preserving case, this yields that the system is topologically
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Optimal Recovery of Operators in Function L -Spaces Anal. Math. (IF 0.527) Pub Date : 2021-01-16 V. Babenko, V. Babenko, O. Kovalenko, M. Polishchuk
We consider the classes of functions that are defined on a metric compact, take values in an L-space (i.e. semi-isotropic semi-linear metric space) and have a given majorant of modulus of continuity. For a wide class of operators Λ that act on such function classes, we solve the problem of the optimal recovery based on inaccurate values of the functions in a finite number of points. As an application
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Non-Spectral Problem on Infinite Bernoulli Convolution Anal. Math. (IF 0.527) Pub Date : 2021-01-16 Q. Li, Z.-Y. Wu
Let \(\left\{ {{d_k}} \right\}_{k = 1}^\infty \) be an upper-bounded sequence of positive integers and let δE be the uniformly discrete probability measure on the finite set E. For 0 < ρ < 1, the infinite convolution \({\mu _{\rho \left\{ {0,{d_k}} \right\}}}: = {\delta _{\rho \left\{ {0,{d_1}} \right\}}}*{\delta _{{\rho ^2}\left\{ {0,{d_2}} \right\}}}* \cdots \) is called an infinite Bernoulli convolution
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On the Distribution of Meromorphic Functions of Positive Hyper-Order Anal. Math. (IF 0.527) Pub Date : 2021-01-16 P. Yang, S. Wang
Let f(z) be a transcendental meromorphic function, whose zeros have multiplicity at least 3. Set α(z): = β(z)exp (γ(z), where β(z) is a nonconstant elliptic function and γ(z) is an entire function. If σ(f(z)) > σ(α(z)), then f′(z) = α(z) has infinitely many solutions in the complex plane.
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Boundedness and Compactness of Commutators for Bilinear Fractional Integral Operators on Morrey Spaces Anal. Math. (IF 0.527) Pub Date : 2021-01-16 Q. Guo, J. Zhou
We show a characterization for the boundedness of the commutators for bilinear fractional integral operators Bα (0 < α < n) on Morrey spaces. Moreover, we obtain that if b ∈ CMO, then the commutators [b, Bα]i (i = 1, 2) are separately compact operators on Morrey spaces where CMO denotes the BMO-closure of C ∞c (ℝn). A necessary condition for commutators [b, Bα]i (i = 1, 2) to be jointly compact on
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Efficient Presentations of Relative Cuntz-Krieger Algebras Anal. Math. (IF 0.527) Pub Date : 2021-01-16 L. O. Clark, Y. E. P. Pangalela
In this article, we present a new method to study relative Cuntz-Krieger algebras for higher-rank graphs. We only work with edges rather than paths of arbitrary degrees. We then use this method to simplify the existing results about relative Cuntz-Krieger algebras. We also give applications to study ideals and quotients of Toeplitz algebras.
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Some Properties of General Fourier Coefficients of Lipschitz Functions Anal. Math. (IF 0.527) Pub Date : 2021-01-05 V. Tsagareishvili
In this paper, the properties of Lipschitz functions are considered and the convergence of the special type of series of Fourier coefficients with respect to general orthonormal systems (ONS) is investigated. For the functions of ONS we find a condition under which the special series of Fourier coefficients of Lipschitz functions with respect to general orthonormal systems are convergent. The obtained
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Good Behaviour of Lie Bracket at a Superdensity Point of the Tangency Set of a Submanifold With Respect to a Rank 2 Distribution Anal. Math. (IF 0.527) Pub Date : 2021-01-05 S. Delladio
Let H, K be a couple of vector fields of class C1 in an open set U ⊂ ℝN+m, \({\cal M}\) be a N-dimensional C1 submanifold of U and define \({\cal T}: = \left\{{z \in {\cal M}:H\left(z \right),K\left(z \right) \in {T_z}{\cal M}} \right\}\). Then the obvious property If z0 ∈ \({\cal M}\) is an interior point (relative to \({\cal M}\))of \({\cal T}\) then \(\left[{H,K} \right]\left({{z_0}} \right) \in
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On a Result of Bhayo and Sándor Anal. Math. (IF 0.527) Pub Date : 2021-01-02 Y. J. Bagul
We point out that the proof of Theorem 1.6 in the paper [2] by B. A. Bhayo and J. Sándor contains a mistake. Correcting this mistake is the main aim of this note.
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Real Zeros of Random Cosine Polynomials with Palindromic Blocks of Coefficients Anal. Math. (IF 0.527) Pub Date : 2021-01-02 A. Pirhadi
It is well known that a random cosine polynomial \({V_n}\left(x \right) = \sum\nolimits_{j = 0}^n {{a_j}\cos \left({jx} \right)} \), x ∈ (0, 2π), with the coefficients being independent and identically distributed (i.i.d.) real-valued standard Gaussian random variables (asymptotically) has \(2n/\sqrt 3 \) expected real roots. On the other hand, out of many ways to construct a dependent random polynomial
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BSE Properties of Some Banach Function Algebras Anal. Math. (IF 0.527) Pub Date : 2021-01-02 Z. S. Hosseini, E. Feizi, A. H. Sanatpour
In this paper, BSE properties of some Banach function algebras are studied. We show that Lipschitz algebras Lipα (X, d) and Dales-Davie algebras D(X, M) are BSE-algebras for certain underlying plane sets X. Moreover, we investigate BSE properties of certain subalgebras of Lipα(X, d)suchas LipA (X, α), Lipn (X, α) and Lip(X, M, α). BSE properties of Bloch type spaces \({{\cal B}_\alpha}\) and Zygmund
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Value distribution of q -differences of meromorphic functions in several complex variables Anal. Math. (IF 0.527) Pub Date : 2020-11-18 T.-B. Cao, R. J. Korhonen
In this paper, we study q-difference analogues of several central results in value distribution theory of several complex variables such as q-difference versions of the logarithmic derivative lemma, the second main theorem for hyperplanes and hypersurfaces, and a Picard type theorem. Moreover, the Tumura–Clunie theorem concerning partial q-difference polynomials is also obtained. Finally, we apply
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Weighted approximation of functions in L p -norm by Baskakov-Kantorovich operator Anal. Math. (IF 0.527) Pub Date : 2020-11-18 P. E. Parvanov
We investigate the weighted approximation of functions in Lp-norm by Kantorovich modifications of the classical Baskakov operator, with weights of type (1+x)α, α ∈ ℝ. By defining an appropriate K-functional we prove direct inequalities for them.
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Hypergeometric Representations and Differential-Difference Relations for Some Kernels Appearing in Mathematical Physics Anal. Math. (IF 0.527) Pub Date : 2020-08-20 D. B. Karp; Y. B. Melnikov; I. V. Turuntaeva
We investigate the analytic properties of a new class of special functions that appear in the kernels of a class of integral operators underlying the dynamics of matter relaxation processes in attractive fields. These functions, recently introduced by the second author, generate the kernels of the principal parts of these operators and play an important role in understanding their spectral characteristics
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On the Commutators of Marcinkiewicz Integrals with Rough Kernels in Weighted Lebesgue Spaces Anal. Math. (IF 0.527) Pub Date : 2020-08-20 Y.-M. Wen; H.-X. Wu
This paper is devoted to studying the boundedness and compactness of commutators for Marcinkiewicz integrals with rough kernels in weighted Lebesgue spaces. The characterized theorems on the boundedness and compactness for such commutators are established, respectively. We improve and extend the previous results. Meanwhile, the quantitative weighted bounds for the commutator of Marcinkiewicz integral
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Balian–Low Type Theorems on Homogeneous Groups Anal. Math. (IF 0.527) Pub Date : 2020-08-20 K. Gröchenig; J. L. Romero; D. Rottensteiner; J. T. Van Velthoven
We prove strict necessary density conditions for coherent frames and Riesz sequences on homogeneous groups. Let N be a connected, simply connected nilpotent Lie group with a dilation structure (a homogeneous group) and let (π,Hπ) be an irreducible, square-integrable representation modulo the center Z(N) of N on a Hilbert space Hπ of formal dimension dπ. If g ∈ Hπ is an integrable vector and the set
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Sendov’s Conjecture: A Note on a Paper of Dégot Anal. Math. (IF 0.527) Pub Date : 2020-08-20 T. P. Chalebgwa
Sendov’s conjecture states that if all the zeroes of a complex polynomial P(z) of degree at least two lie in the unit disk, then within a unit distance of each zero lies a critical point of P(z). In a paper that appeared in 2014, Dégot proved that, for each a ∈ (0, 1), there exists an integer N such that for any polynomial P(z) with degree greater than N, if P(a) = 0 and all zeroes lie inside the unit
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On the Absence of Stability of Bases in Some Fréchet Spaces Anal. Math. (IF 0.527) Pub Date : 2020-08-18 A. Goncharov
We show that, for each compact subset of the real line of infinite cardinality with an isolated point, the space of Whitney jets on the set does not possess a basis consisting only of polynomials. On the other hand, polynomials are dense in any Whitney space. Thus, there are no general results about stability of bases in Fréchet spaces.
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A Multidimensional Analogue of the A. N. Tikhonov’s Theorem on Calculating Values of a Function with Respect to Approximately Given Fourier Coefficients Anal. Math. (IF 0.527) Pub Date : 2020-08-18 F. B. Benli, O. A. İilhan, Sh. G. Kasimov, G. S. Xaitboyev
In this paper, we study the problem of approximation to reconstruct the value of a function of several variables from the approximate values of the Fourier coefficients of a function at a given fixed point. A theorem on the reconstruction of the value of a function with several variables at any given fixed point with a small error is given.
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Meromorphic Functions that Share Values with their Shifts or their n -th Order Differences Anal. Math. (IF 0.527) Pub Date : 2020-08-18 X.-G. Qi, L.-Z. Yang
Let f(z) be a non-constant meromorphic (entire) function of hyper-order strictly less than 1, n ≥ 3 (n ≥ 2) be an integer. It is shown that if fn(z) and fn(z + c) share a(≠ 0) ∈ ℂ and ∞ CM, then f(z) = t1f(z + c) or f(z) = t2f(z + 2c), where t1 and t2 satisfy \(t_i^n=1\), (i = 1, 2). Some examples are provided to show the sharpness of our results. In addition, we mainly obtain two uniqueness results
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New Kantorovich Type Inequalities for Negative Parameters Anal. Math. (IF 0.527) Pub Date : 2020-08-18 S. Furuichi, H. R. Moradi
We show the following result: Let \(A, B \in \mathbb{B}(\mathcal{H})\) be two strictly positive operators such that A ≤ B and \(m1_{\mathcal{H}}\leq{B}\leq{M1_{\mathcal{H}}}\) for some scalars 0 < m < M. Then $$B^p\leq{\rm{exp}}(\frac{M1_{\mathcal{H}}-B}{M-m}{\rm{ln}} \;m^p+\frac{B-m1_{\mathcal{H}}}{M-m}{\rm{ln}} \;M^p)\leq{K(m, M, p, q)}A^q$$ for p ≤ 0, −1 ≤ q ≤ 0 where K(m, M, p, q) is the generalized
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On the Probability that the Maximum of a Polynomial is at an Endpoint of an Interval Anal. Math. (IF 0.527) Pub Date : 2020-08-18 L. Bos, T. Ware
In this article we study the probability that the maximum over a symmetric interval [−a, a] of a univariate polynomial of degree at most n is attained at an endpoint. We give explicit formulas for the degree n = 1, 2,3 cases. The formula for the degree 3 case leads to a lower bound for the true probability. Numerical experiments indicate that this lower bound is actually quite a good approximation
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Zeros of Complex Polynomials and Kaplan Classes Anal. Math. (IF 0.527) Pub Date : 2020-08-05 Sz. Ignaciuk, M. Parol
We carry out complete membership to Kaplan classes of polynomials with all zeros on unit circle. In this way we extend Sheil-Small’s and Jahangiri’s theorems.
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Local Wiener’s Theorem and Coherent Sets of Frequencies Anal. Math. (IF 0.527) Pub Date : 2020-08-05 S. Yu. Favorov
Using a local analogue of the Wiener-Levi theorem, we investigate the class of measures on Euclidean space with discrete support and spectrum. Also, we find a new sufficient conditions for a discrete set in Euclidean space to be a coherent set of frequencies.
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C -Robin Functions and Applications Anal. Math. (IF 0.527) Pub Date : 2020-08-05 N. Levenberg, S. Ma’u
We continue the study in [1] in the setting of pluripotential theory arising from polynomials associated to a convex body C in (ℝ+)d. Here we discuss C-Robin functions and their applications. In the particular case where C is a triangle in (ℝ+)2 with vertices (0, 0), (b, 0), (0, a), a, b > 0, we generalize results of T. Bloom to construct families of polynomials which recover the C-extremal function
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Optimal Recovery of a Derivative of an Analytic Function from Values of the Function Given with an Error on a Part of the Boundary. II Anal. Math. (IF 0.527) Pub Date : 2020-08-05 R. R. Akopyan
We continue the study of several related extremal problems for functions analytic in a simply connected domain G with a rectifiable Jordan boundary Γ. In particular, the problem of optimal recovery of a derivative at a point z0 ∈ G from limit boundary values given with an error on a measurable part γ1 of the boundary Γ for the class Q of functions with limit boundary values bounded by 1 on γ0 = Γ γ1
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Extremals for a Trudinger-Moser Inequality with a Vanishing Weight in the Unit Disk Anal. Math. (IF 0.527) Pub Date : 2020-08-05 M. Zhang
In this paper, we study a Trudinger-Moser inequality with a vanishing weight in the unit disk. Precisely, let \(B\) be the unit disk and β ≥ 0 be a real number. Denote \({\cal S} = \left\{{u \in W_0^{1,2}\left(B\right);u} \right.\) is a radially symmetric function and ∥∇u∥2≤ 1. Suppose a function h(x) is radially symmetric, nonnegative, continuous on \(\overline{\mathbb{B}}\) and satisfies h(x) > 0
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Uniform Approximation of Differentiation Operators by Bounded Linear Operators in the Space L r Anal. Math. (IF 0.527) Pub Date : 2020-08-05 V. Arestov
We discuss the problem of the best uniform approximation on the axis, i.e., in the space C(−∞,∞), of the differentiation operator of order k on the class of functions with bounded derivative of order n, 0 < k < n, by bounded linear operators in the space Lr,1 ≤ r < ∞. We give an exact solution of the problem for odd n ≥ 3 and all k, 0 < k < n. For even n, a result close to the best one is obtained
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Sharp Two-Sided Estimate for the Sum of a Sine Series with Convex Slowly Varying Sequence of Coefficients Anal. Math. (IF 0.527) Pub Date : 2020-08-05 A. P. Solodov
The sum of a sine series \(g\left({b,x} \right) = \sum\nolimits_{k = 1}^\infty {}\)bk sin kx with coefficients forming a convex sequence b is known to be positive on the interval (0,π). To estimate its values near zero Telyakovskiĭ used the piecewise-continuous function \(\sigma \left({{\bf{b}},x} \right) = \left({1/m\left(x \right)} \right)\sum\nolimits_{k = 1}^{m\left(x \right) - 1} {{k^2}\left({{b_k}
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Stationary Phase Type Estimates for Low Symbol Regularity Anal. Math. (IF 0.527) Pub Date : 2020-06-17 M. Tacy
The well-known stationary phase formula gives us a way to find asymptotics of oscillating integrals so long as the symbol is regular enough (in comparison to the large parameter controlling the oscillation). However in a number of applications we find ourselves with symbols that are not suitably regular. In this paper we obtain decay bounds for such oscillatory integrals.
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Difference of Weighted Composition Operators on Weighted-Type Spaces in the Unit Ball Anal. Math. (IF 0.527) Pub Date : 2020-06-17 B. Hu; S. Li
In this paper, a new characterization is provided for the boundedness, compactness and essential norm of the difference of two weighted composition operators on weighted-type spaces in the unit ball of ℂn.
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On Maximally Oscillating Perfect Splines and Some of Their Extremal Properties Anal. Math. (IF 0.527) Pub Date : 2020-06-17 O. Kovalenko
In this paper we study analogues of the perfect splines for weighted Sobolev classes of functions defined on the half-line. Maximally oscillating splines play important role in the solution of certain extremal problems. In particular, using these splines, we characterize the modulus of continuity of the differential operator.
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The (Generalized) Weylness of Upper Triangular Operator Matrices Anal. Math. (IF 0.527) Pub Date : 2020-06-17 J. Dong; X. H. Cao
Let ℋ and \({\cal K}\) be complex infinite dimensional separable Hilbert spaces. We denote by \({M_C} = \left( {\begin{array}{*{20}{c}} A&C \\ 0&B \end{array}} \right)\) a 2 × 2 upper triangular operator matrix acting on \({\cal H} \oplus {\cal K}\), where \(A \in {\cal B}\left({\cal H} \right),\,B \in {\cal B}\left({\cal K} \right)\) and \(C \in {\cal B}\left({{\cal K},{\cal H}} \right)\). In this
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Bilinear estimates on Morrey spaces by using average Anal. Math. (IF 0.527) Pub Date : 2020-05-15 N. Hatano
This paper is a follow up of a recent work of the author and Y. Sawano [6], in 2019. We investigate the boundedness of the bilinear fractional integral operator introduced by Grafakos in [3], 1992. When the local integrability index s falls 1 with weights and t exceeds 1, He and Yan obtained some results on this operator was worked on Morrey spaces earlier in [7] 2018. Later in the paper [6] we considered
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Meromorphic solutions on the first order non-linear difference equations Anal. Math. (IF 0.527) Pub Date : 2020-05-15 J. Li; K. Liu
Steinmetz [16] considered the first order non-linear differential equations$$C(z, f)(f^\prime)^2+B(z, f)f^\prime+A(z, f)=0,$$where A(z, f), B(z, f), C(z, f) are polynomials in f with rational coefficients in z and pointed out that the above equation must reduce into some certain types when it admits transcendental meromorphic solutions. In this paper, we will consider its difference version$$C(z, f)f(z+c)^2+B(z
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Compactness of Hankel operator with symbols of forms Anal. Math. (IF 0.527) Pub Date : 2020-05-15 X. Cheng; M. Jin; Q. Wang
We consider the Hankel operator with symbols of forms and study the relationship between the compactness of this operator and the compactness of ∂̄-Neumann operator.
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B -Fredholm linear relations in Hilbert spaces Anal. Math. (IF 0.527) Pub Date : 2020-05-15 A. Ghorbel; M. Mnif
In this paper, B-Fredholm linear relations in Hilbert spaces are introduced and some of their properties are given. In particular, it is shown that they are completely characterized in terms of an algebraic decomposition with a Fredholm linear relation and a bounded nilpotent operator. The behaviour of a polynomial in them is also investigated.
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Unconditional bases of wavelets in local fields Anal. Math. (IF 0.527) Pub Date : 2020-05-15 B. Behera
We provide sufficient conditions on the wavelets on a local field K for the wavelet system to form an unconditional basis for the Hardy space H1(K) and the Lebesgue spaces Lp(K), 1 < p < ∞.
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Symmetries for J -projection Anal. Math. (IF 0.527) Pub Date : 2020-05-15 X.-M. Xu; Y. Li
Let \(\mathcal{B}(\mathcal{H})\) be the algebra of all bounded linear operators on a separable complex Hilbert space \(\mathcal{H}\). We introduce the J-decomposition property for projections in \(\mathcal{B}(\mathcal{H})\), and prove that the projection E in \(\mathcal{B}(\mathcal{H})\) has J-decomposition property with respect to a particular space decomposition, which is related to Hal-mos’ two
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Extremal growth of polynomials Anal. Math. (IF 0.527) Pub Date : 2020-05-15 L. Bos; S. Ma’u; S. Waldron
We give an exposition of some simple but applicable cases of worst-case growth of a polynomial in terms of its uniform norm on a given compact set K ⊂ ℂd. Included is a direct verification of the formula for the pluripotential extremal function for a real simplex. Throughout we attempt to make the exposition as accessible to a general (analytic) audience as possible, avoiding wherever possible the
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Generation of relatively uniformly continuous semigroups on vector lattices Anal. Math. (IF 0.527) Pub Date : 2020-04-05 M. Kaplin; M. Kramar Fijavž
We prove a Hille–Yosida type theorem for relatively uniformly continuous positive semigroups on vector lattices. We introduce the notions of relatively uniformly continuous, differentiable, and integrable functions on ℝ+. These notions allow us to study the generators of relatively uniformly continuous semigroups. Our main result provides sufficient and necessary conditions for an operator to be the
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Some inequalities involving Heron and Heinz means of two convex functionals Anal. Math. (IF 0.527) Pub Date : 2020-04-05 M. Raïssouli; S. Furuichi
In this paper we first introduce the Heron and Heinz means of two convex functionals. Afterwards, some inequalities involving these functional means are investigated. The operator versions of our theoretical functional results are immediately deduced. We also obtain new refinements of some known operator inequalities via our functional approach in a fast and nice way.
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Universal functions with respect to the double Walsh system for classes of integrable functions Anal. Math. (IF 0.527) Pub Date : 2020-04-05 A. Sargsyan; M. Grigoryan
The paper addresses questions on existence and structure of universal functions for spaces L1(E), E ⊂ [0, 1)2, with respect to the doubleWalsh system in the sense of signs of Fourier coefficients. It is shown that for each ε > 0 one can find a measurable set Eε ⊂ [0, 1)2 with measure |Eε| > 1−ε, such that by a proper modification of any integrable function f ∈ L1[0, 1)2 outside Eε one can get an integrable
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Convolution operators on Banach–Orlicz algebras Anal. Math. (IF 0.527) Pub Date : 2020-04-03 A. Ebadian; A. Jabbari
For a locally compact group G, let \(\mathcal{L}^{\Phi}\)(G) and \(\mathcal{L}_\omega^{\Phi}\)(G) be Orlicz and weighted Orlicz spaces, respectively, where Φ is a Young function and ω is a weight on G. We study the harmonic and convolution operators on Orlicz and weighted Orlicz spaces. We prove that under some conditions the harmonic operators on \(\mathcal{L}^{\Phi}\)(G) and \(\mathcal{L}_\omega^{\Phi}\)(G)
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ACC Conjecture for Weighted Log Canonical Thresholds Anal. Math. (IF 0.527) Pub Date : 2020-02-14 N. X. Hong; T. V. Long; P. N. T. Trang
In this paper, we study the weight log canonical thresholds of holomorphic functions. We prove the ascending chain condition for certain weight in dimension two.
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No Entire Inner Functions Anal. Math. (IF 0.527) Pub Date : 2020-02-14 A. Cobos; D. Seco
We study generalized inner functions on a large family of Reproducing Kernel Hilbert Spaces. We show that the only inner functions which are entire are the normalized monomials.
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ℓ p -Improving Inequalities for Discrete Spherical Averages Anal. Math. (IF 0.527) Pub Date : 2020-02-14 R. Kesler; M. T. Lacey
Let λ2 ∈ ℕ, and in dimensions d ≥ 5, let Aλf(x) denote the average of f: ℤd → ℝ over the lattice points on the sphere of radius λ centered at x. We prove ℓp improving properties of Aλ:$$\begin{array}{*{20}{c}} {{{\left\| {{A_\lambda }} \right\|}_{{\ell ^{p \to }}{\ell ^{p'}}}} \leqslant {C_{d,p,\omega ({\lambda ^2})}}{\lambda ^{(1 - \tfrac{2}{p})}},}&{\frac{{d - 1}}{{d + 1}} < p \leqslant \frac{d}{{d
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Commutators of Bilinear θ -Type Calderón–Zygmund Operators on Morrey Spaces Over Non-Homogeneous Spaces Anal. Math. (IF 0.527) Pub Date : 2020-02-14 G.-H. Lu
The aim of this paper is to establish the boundedness of the commutator [b1, b2, Tθ], which generated by the bilinear θ-type Calderón–Zygmund operators Tθ and the functions \(b_1, b_2 \in \widetilde {RBMO}(\mu)\), on non-homogeneous metric measure space satisfying the so-called geometrically doubling and the upper doubling conditions. Under the assumption that the dominating function λ satisfies the
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p -Convergent Operators and the p -Schur Property Anal. Math. (IF 0.527) Pub Date : 2020-02-14 M. Alikhani; M. Fakhar; J. Zafarani
In this article we obtain a characterization of the class of p-convergent operators between two Banach spaces in terms of p-(V) subsets of the dual space. Also, for 1 ≤ p < q ≤ ∞, by introducing the concepts of Pelczyński's properties (V)p,q and (V*)p,q, we obtain a condition that ensures that q-convergent operators are p-convergent operators. Some characterizations of the p-Schur property of Banach
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Lusin Characterisation of Hardy Spaces Associated with Hermite Operators Anal. Math. (IF 0.527) Pub Date : 2020-02-14 T. D. Do; N. N. Trong; L. X. Truong
Let d ∈ {3, 4, 5,...} and p ∈ (0, 1]. We consider the Hermite operator L = −Δ + |x|2 on its maximal domain in L2(ℝd). Let \(H_L^p(\mathbb{R}^d)\) be the completion of \(\left\{ {f \in {L^2}({\mathbb{R}^d}):{\mathcal{M}_L}f \in {L^p}({\mathbb{R}^d})} \right\}\) with respect to the quasi-norm \({\left\| \cdot \right\|_{H_L^p}} = {\left\| {{\mathcal{M}_L} \cdot } \right\|_{{L^p}}}\), where \({\mathcal{M}_L}f(
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On Some Properties of Relative Capacity and Thinness in Weighted Variable Exponent Sobolev Spaces Anal. Math. (IF 0.527) Pub Date : 2020-02-14 C. Unal; I. Aydin
We define the weighted relative p(.)-capacity and discuss its properties in the space \(W_\vartheta ^{1,p(.)}({\mathbb{R}^n})\). Also, we investigate some properties of the weighted variable Sobolev capacity. It is shown that there is a relation between these two capacities. Moreover, we introduce the notion of thinness related to this newly defined relative capacity and prove an equivalence statement
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Maximal Operators and Characterization of Hardy Spaces Anal. Math. (IF 0.527) Pub Date : 2020-02-14 N. Memić; S. Sadiković
It is known that the maximal operator σ* ƒ is of type (Hp,Lp) if the Vilenkin group G is bounded and \(p > \tfrac{1}{2}\). We prove a maximal converse inequality which characterizes the space Hp by means of the operator σ†ƒ:= supn |σMnƒ|, for bounded groups.
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Classical Orthogonal Polynomials and Some New Properties for Their Centroids of Zeroes Anal. Math. (IF 0.527) Pub Date : 2020-02-14 B. Aloui; W. Chammam
This paper aims to highlight new properties of the centroid of the zeroes of a polynomial. As an illustration, we apply these techniques to O-classical orthogonal polynomials, where O is the derivative operator D or the q-derivative Hq.
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A Lower Bound for the Maximum of a Polynomial in the Unit Disc Anal. Math. (IF 0.527) Pub Date : 2020-02-14 A. Dubickas
In this paper we show that the maximum of a polynomial P ∈ ℂ[z] of degree d ≥ 2 in the unit disc can be bounded below by the sum of moduli of its two coefficients, say, for zs and zt under certain assumption on the pair s < t. We also show that this assumption on s, t cannot be removed or weakened and give several examples showing when this lower bound is (or is not) attained.
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On the Invertibility of the Sum of Operators Anal. Math. (IF 0.527) Pub Date : 2020-02-14 M. H. Mortad
The primary purpose of this paper is to investigate the question of the invertibility of the sum of operators in the bounded and unbounded setting. Some interesting examples and consequences are given. As an illustrative point, we characterize invertibility for the class of normal operators. Also, we give a very short proof of the self-adjointness of a normal operator which has a real spectrum.
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A Prime Geodesic Theorem of Gallagher Type for Riemann Surfaces Anal. Math. (IF 0.527) Pub Date : 2020-02-14 M. Avdispahić
We consider a cofinite Fuchsian group of the first kind with finitely many inequivalent parabolic elements and a unitary multiplier system of an arbitrary weight on it. Through the Gallagher–Koyama approach to the prime geodesic theorem on the corresponding noncompact hyperbolic surface, we reduce the exponent in the error term from \(\frac{3}{4}\) to \(\frac{7}{10}\) outside a set of finite logarithmic
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Duals of Hardy Amalgam Spaces and Norm Inequalities Anal. Math. (IF 0.527) Pub Date : 2019-12-16 Z. V. P. Ablé; J. Feuto
We characterize the dual spaces of the generalized Hardy spaces defined by replacing Lebesgue quasi-norms by Wiener amalgam ones. In these generalized Hardy spaces we prove that some classical linear operators such as Calderón–Zygmund, convolution and Riesz potential operators are bounded.
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Sharp Inequalities for the Numerical Radii of Block Operator Matrices Anal. Math. (IF 0.527) Pub Date : 2019-12-16 M. Ghaderi Aghideh; M. S. Moslehian; J. Rooin
In this paper we present several sharp upper bounds for the numerical radii of the diagonal and off-diagonal parts of the 2×2 block operator matrix \(\left[ {\begin{array}{*{20}{c}} A&B \\ C&D \end{array}} \right]\). Among extensions of some results of Kittaneh et al., it is shown that if \(T = \left[ {\begin{array}{*{20}{c}} A&0 \\ 0&D \end{array}} \right]\), and f and g are non-negative continuous
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Bounds on Autocorrelation Coefficients of Rudin-Shapiro Polynomials Anal. Math. (IF 0.527) Pub Date : 2019-12-16 J.-P. Allouche; S. Choi; A. Denise; T. Erdélyi; B. Saffari
We study the autocorrelation coefficients of the Rudin–Shapiro polynomials, proving in particular that their maximum on the interval [1, 2n) is bounded from below by C12αn and is bounded from above by C22α’n where α = 0.7302852 ... and α′ = 0.7302867....
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Calculus and Nonlinear Integral Equations for Functions with Values in L -Spaces Anal. Math. (IF 0.527) Pub Date : 2019-12-16 V. Babenko
In this paper, the calculus of functions with values in L-spaces is developed. We then consider nonlinear integral equations of Fredholm and Volterra types for functions with values in L-spaces. Such class of equations includes set-valued integral equations, fuzzy integral equations, and many others. We prove theorems of existence and uniqueness of the solutions of such equations and investigate data
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