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Periodic and almost periodic motions of Navier–Stokes flows and their stability in a perturbed half-space Anal. Math. Phys. (IF 1.7) Pub Date : 2024-03-16
Abstract Consider the system of Navier–Stokes equations in a perturbed half-space. We study the existence and stability of periodic solutions and almost periodic solutions to this system. For the Stokes system we use \(L^p\text {-}L^q\) estimates in combination with interpolation spaces to show the existence of bounded (in time) mild solutions as well as the existence of periodic solutions. Moreover
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Structural transitions in interacting lattice systems Anal. Math. Phys. (IF 1.7) Pub Date : 2024-03-15
Abstract We consider two-dimensional systems of point particles located on rectangular lattices and interacting via pairwise potentials. The goal of this paper is to investigate the phase transitions (and their nature) at fixed density for the minimal energy of such systems. The 2D rectangle lattices we consider have an elementary cell of sides a and b, the aspect ratio is defined as \(\Delta =b/a\)
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The generalization of strong anisotropic XXZ model and UC hierarchy Anal. Math. Phys. (IF 1.7) Pub Date : 2024-03-13
Abstract This paper is concerned with the construction of the generalized strong anisotropic XXZ model. By means of the quantum inverse scattering method and boson-fermion correspondence, we investigate the general states and the scalar products of general states in the generalized strong anisotropic XXZ model which are tau functions of the universal character hierarchy. In addition, the relations
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A new class of weights associated with Schrödinger operator on Heisenberg groups and applications Anal. Math. Phys. (IF 1.7) Pub Date : 2024-03-12 Nguyen Ngoc Trong, Nguyen Xuan Viet Trung, Le Xuan Truong, Tan Duc Do
We extend the new class of Euclidean weights constructed by Bongioanni et al. (J Math Anal Appl 373:563–579, 2011) to the setting of Heisenberg groups. Then we show that various well-known operators are bounded on the corresponding new weighted Lebesgue spaces. The process of proving these results produces several interesting estimates of independent interest.
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Density of states for the Anderson model on nested fractals Anal. Math. Phys. (IF 1.7) Pub Date : 2024-03-10 Hubert Balsam, Kamil Kaleta, Mariusz Olszewski, Katarzyna Pietruska-Pałuba
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Inverse spectral problems for Dirac-type operators with global delay on a star graph Anal. Math. Phys. (IF 1.7) Pub Date : 2024-03-10 Feng Wang, Chuan-Fu Yang, Sergey Buterin, Nebojs̆a Djurić
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Existence, uniqueness and decay rates of a certain type of 3D Hall-MHD equations with power-law type Anal. Math. Phys. (IF 1.7) Pub Date : 2024-03-04 Jae-Myoung Kim
We investigate the local-in-time existence results of classical solutions to the 3D (Hall-)MHD equations with power-law type nonlinear viscous fluid when magnetic resistance is vanished and also show the global-in-time existence of classical solutions under small initial data. Moreover, we prove the space-time decay property for these solutions.
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A primer on eigenvalue problems of non-self-adjoint operators Anal. Math. Phys. (IF 1.7) Pub Date : 2024-03-04
Abstract Non-self adjoint operators describe problems in science and engineering that lack symmetry and unitarity. They have applications in convection–diffusion processes, quantum mechanics, fluid mechanics, optics, wave-guide theory, and other fields of physics. This paper reviews some important aspects of the eigenvalue problems of non-self-adjoint differential operators and discusses the spectral
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Pólya–Szegö type inequality and imbedding theorems for weighted Sobolev spaces Anal. Math. Phys. (IF 1.7) Pub Date : 2024-03-04 N. Q. Nga, N. M. Tri, D. A. Tuan
In this paper we will establish a new Pólya–Szegö type inequality for a weighted gradient of a function on \({\mathbb {R}}^2\) with respect to a weighted area. In order to do that we need to study an isoperimetric problem for the weighted area. We then apply the inequality to prove embedding theorems for weighted Sobolev spaces and to calculate the best constant in the Sobolev imbedding theorems. In
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Spiked solutions for fractional Schrödinger systems with Sobolev critical exponent Anal. Math. Phys. (IF 1.7) Pub Date : 2024-02-26 Wenjing Chen, Xiaomeng Huang
In this article, we study the following fractional critical Schrödinger system $$\begin{aligned} {\left\{ \begin{array}{ll} (-\Delta )^s u_i=\mu _iu_i^3+\beta u_i\sum _{j\ne i}u_j^{2}+\lambda _iu_i &{}\text { in } \ \Omega ,\\ u_i=0 &{}\text { on } \ {\mathbb {R}}^N\setminus \Omega , \end{array}\right. } \quad i=1,2,\ldots ,m, \end{aligned}$$ where \(00\), coupling constant \(\beta \) satisfies either
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Topological properties of certain iterated entire maps Anal. Math. Phys. (IF 1.7) Pub Date : 2024-02-26 Chunlei Cao, Yuefei Wang, Huayu Zhao
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On sequences preserving q-Gevrey asymptotic expansions Anal. Math. Phys. (IF 1.7) Pub Date : 2024-02-21
Abstract The modification of the coefficients of formal power series is analyzed in order that such variation preserves q-Gevrey asymptotic properties, in particular q-Gevrey asymptotic expansions. A characterization of such sequences is determined, providing a handy tool in practice. The sequence of q-factorials is proved to preserve q-Gevrey asymptotic expansions.
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Eigenvalue for a problem involving the fractional (p, q)-Laplacian operator and nonlinearity with a singular and a supercritical Sobolev growth Anal. Math. Phys. (IF 1.7) Pub Date : 2024-02-13 A. L. A. de Araujo, A. H. S. Medeiros
In this paper, we are interested in studying the multiplicity, uniqueness, and nonexistence of solutions for a class of singular elliptic eigenvalue problems for the Dirichlet fractional (p, q)-Laplacian. The nonlinearity considered involves supercritical Sobolev growth. Our approach is variational together with the sub- and supersolution methods, and in this way we can address a wide range of problems
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Applications of Jack’s lemma Anal. Math. Phys. (IF 1.7) Pub Date : 2024-02-12 Mamoru Nunokawa, Krzysztof Piejko, Janusz Sokół
In the Jack’s lemma it is considered q(z), an analytic function in \(|z|<1\) with \(q(0)=0\) for which |q(z)| attains its maximum value on the disc \(|z|\le r<1\) at the point \(z_0\), \(|z_0|=r\). Then \(z_0q'(z_0)=kq(z_0)\) and \(k\ge 1\). In this paper we try to say more about the number k in a generalizations of this lemma, where we consider \(\max |\arg \{q(z)\}|\) or \(\min |\mathfrak {Re} \{q(z)\}|\)
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Mild solution for the time fractional magneto-hydrodynamics system Anal. Math. Phys. (IF 1.7) Pub Date : 2024-02-08 Hassan Khaider, Achraf Azanzal, Raji Abderrahmane, Melliani Said
In this paper, by using the Mittag–Leffler operators \(\{\mathcal {L}_{\alpha }(-t^{\alpha }\mathbb {I}):t\ge 0\}\) and \(\{\mathcal {L}_{\alpha ,\alpha }(-t^{\alpha }\mathbb {I}):t\ge 0\}\) we will prove the mild soltion of the time fractional magneto-hydrodynamics system with a fractional derivative of Caputo. Furthermore, by Itô integral, we will establish the mild solution of stochastic time fractional
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Cwikel–Lieb–Rozenblum inequalities for the Coulomb Hamiltonian Anal. Math. Phys. (IF 1.7) Pub Date : 2024-02-07 Andrés Díaz Selvi
We prove sharp Cwikel–Lieb–Rozenblum type inequalities for the Coulomb Hamiltonian in dimension higher than five. We furthermore show that the classical constant obtained from Weyl asymptotics doesn’t hold in dimensions four and five.
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Variation type characterization of product Hardy spaces Anal. Math. Phys. (IF 1.7) Pub Date : 2024-02-06
Abstract In the multidimensional Euclidean space, except the classical real Hardy space, there are numerous product ones. We associate with each of them a class of functions related to the known variations and new ones. Such a characterization is fulfilled by means of the integrability of the Fourier transform
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Bernstein’s inequalities and Jackson’s inverse theorems in the Laguerre hypergroup Anal. Math. Phys. (IF 1.7) Pub Date : 2024-02-03 Othman Tyr
In this research, we investigate some approximation theorems for \( L^{2} \)-space on the Laguerre hypergroup which is the fundamental manifold of the radial functions space for the Heisenberg group. An analogue of Bernstein’s theorem is shown. Some inverse theorems of Jackson–Stechkin in terms of best approximations for the moduli of smoothness defined using generalized translation operators on the
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BMO-regularity for a degenerate transmission problem Anal. Math. Phys. (IF 1.7) Pub Date : 2024-01-24 Vincenzo Bianca, Edgard A. Pimentel, José Miguel Urbano
We examine a transmission problem driven by a degenerate quasilinear operator with a natural interface condition. Two aspects of the problem entail genuine difficulties in the analysis: the absence of representation formulas for the operator and the degenerate nature of the diffusion process. Our arguments circumvent these difficulties and lead to new regularity estimates. For bounded interface data
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A weak solution for the fractional N-Laplacian flow Anal. Math. Phys. (IF 1.7) Pub Date : 2024-01-17 Q-Heung Choi, Tacksun Jung
We deal with the nonlinear parabolic problems given by the fractional N-Laplacian operator and time derivative of functions on the fractional Orlicz–Sobolev spaces. We get a result which shows existence of a weak solution for these fractional N-Laplacian heat flows. We obtain this result by using the approximation method. We first obtain a unique sequence of the approximating weak solutions from the
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Hilbert–Schmidt composition–differentiation operators on the unit ball Anal. Math. Phys. (IF 1.7) Pub Date : 2024-01-12 Ali Abkar
We use the notion of radial differential operator of order \(t>0\) to introduce the weighted composition–differentiation operator \(E^t_{\psi ,\varphi }(f)=\psi \cdot (R^t f)\circ \varphi \) on the Hardy and Bergman spaces of the unit ball and the polydisk in \(\mathbb {C}^n\). We obtain necessary and sufficient conditions on the functions \(\varphi \) and \(\psi \) to ensure that the operator \(E^t_{\psi
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Stability properties of nontrivial periodic water waves for fixed-depth rotational equatorial flows Anal. Math. Phys. (IF 1.7) Pub Date : 2023-12-30 Guowei Dai, Siyu Gao, Ruyun Ma, Yong Zhang
We investigate the local stability for fixed-depth rotational equatorial flows. We first obtain the precise formula of the second derivative of bifurcation parameters at the bifurcation point. In particular, their signs can be assessed when vorticity is small enough and the mean depth is small or large enough. Furthermore, we study the stability property for periodic traveling waves of the thermocline
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Ellipses and polynomial-to-polynomial mapping of weighted Szegő projections Anal. Math. Phys. (IF 1.7) Pub Date : 2023-12-28 Alan R. Legg
We take a look at weighted Szegő projections on ellipses and ellipsoids in light of some known results of real and complex potential theory. We show that on planar ellipses there is a weighted Szegő projection taking polynomials to polynomials without increasing degree.
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Euler–Lagrange–Herglotz equations on Lie algebroids Anal. Math. Phys. (IF 1.7) Pub Date : 2023-12-18 Alexandre Anahory Simoes, Leonardo Colombo, Manuel de León, Modesto Salgado, Silvia Souto
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On the stability of solitary waves in the NLS system of the third-harmonic generation Anal. Math. Phys. (IF 1.7) Pub Date : 2023-12-18 Abba Ramadan, Atanas G. Stefanov
We consider the NLS system of the third-harmonic generation, which was introduced in Sammut et al. (J Opt Soc Am B 15:1488–1496, 1998.). Our interest is in solitary wave solutions and their stability properties. The recent work of Oliveira and Pastor (Anal Math Phys 11, 2021), discussed global well-posedness vs. finite time blow up, as well as other aspects of the dynamics. These authors have also
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Voronovskaja formula for Aldaz–Kounchev–Render operators: uniform convergence Anal. Math. Phys. (IF 1.7) Pub Date : 2023-12-12 Ulrich Abel, Ana Maria Acu, Margareta Heilmann, Ioan Raşa
The Voronovskaja formula for Aldaz–Kounchev–Render operators was established in terms of pointwise convergence. For suitable functions we prove it with uniform convergence. Moreover, we establish the Voronovskaja formula of second order with uniform convergence.
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Positive solutions of biharmonic elliptic problems with a parameter Anal. Math. Phys. (IF 1.7) Pub Date : 2023-12-07 Haiping Chen, Meiqiang Feng
In this article, we analyze the existence, multiplicity and nonexistence of positive solutions for a class of biharmonic equations with Navier boundary conditions and a parameter. In addition, some new criteria for the existence, multiplicity and nonexistence of positive radial solutions for a singular biharmonic equation are also investigated. Our approaches use fixed point theorems on cones.
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Cesàro-like operators acting on a class of analytic function spaces Anal. Math. Phys. (IF 1.7) Pub Date : 2023-12-01 Pengcheng Tang
Let \(\mu \) be a finite positive Borel measure on [0, 1) and let \(H(\mathbb {D})\) be the space of all analytic function in the unit disc \(\mathbb {D}\). The Cesàro-like operator \(\mathcal {C}_\mu \) is defined in \(H(\mathbb {D})\) as follows: If \(f \in H(\mathbb {D})\), \(f(z)=\sum _{n=0}^{\infty }a_{n}z^{n} (z\in \mathbb {D})\), then $$\begin{aligned} \mathcal {C}_\mu (f)(z)=\sum ^\infty _{n=0}\left(
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Besov wavefront set Anal. Math. Phys. (IF 1.7) Pub Date : 2023-11-24 Claudio Dappiaggi, Paolo Rinaldi, Federico Sclavi
We develop a notion of wavefront set aimed at characterizing in Fourier space the directions along which a distribution behaves or not as an element of a specific Besov space. Subsequently we prove an alternative, albeit equivalent characterization of such wavefront set using the language of pseudodifferential operators. Both formulations are used to prove the main underlying structural properties
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On the spectral theory of linear differential-algebraic equations with periodic coefficients Anal. Math. Phys. (IF 1.7) Pub Date : 2023-11-24 Bader Alshammari, Aaron Welters
In this paper, we consider the spectral theory of linear differential-algebraic equations (DAEs) for periodic DAEs in canonical form, i.e., $$\begin{aligned} J \frac{df}{dt}+Hf=\lambda Wf, \end{aligned}$$ where J is a constant skew-Hermitian \(n\times n\) matrix that is not invertible, both \(H=H(t)\) and \(W=W(t)\) are d-periodic Hermitian \(n\times n\)-matrices with Lebesgue measurable functions
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Variation and oscillation for semigroups associated with discrete Jacobi operators Anal. Math. Phys. (IF 1.7) Pub Date : 2023-11-16 J. J. Betancor, M. De León-Contreras
In this paper we prove weighted \(\ell ^p\)-inequalities for variation and oscillation operators defined by semigroups of operators associated with discrete Jacobi operators. Also, we establish that certain maximal operators involving sums of differences of discrete Jacobi semigroups are bounded on weighted \(\ell ^p\)-spaces. \(\ell ^p\)-boundedness properties for the considered operators provide
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On conformal Lorentzian length spaces Anal. Math. Phys. (IF 1.7) Pub Date : 2023-11-16 Neda Ebrahimi, Mehdi Vatandoost, Rahimeh Pourkhandani
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A Fischer type decomposition theorem from the apolar inner product Anal. Math. Phys. (IF 1.7) Pub Date : 2023-11-14 J. M. Aldaz, H. Render
We continue the study initiated by H. S. Shapiro on Fischer decompositions of entire functions, showing that such decomposition exist in a weak sense (we do not prove uniqueness) under hypotheses regarding the order of the entire function f to be expressed as \(f= P\cdot q+r\), the polynomial P, and bounds on the apolar norm of homogeneous polynomials of degree m. These bounds, previously used by Khavinson
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Exotic eigenvalues and analytic resolvent for a graph with a shrinking edge Anal. Math. Phys. (IF 1.7) Pub Date : 2023-10-31 Gregory Berkolaiko, Denis I. Borisov, Marshall King
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A new application of almost increasing sequences to infinite series and Fourier series Anal. Math. Phys. (IF 1.7) Pub Date : 2023-10-27 Hüseyin Bor
Recently, we have obtained two general theorems dealing with \(|\bar{N},p_{n}|_{k}\) summability factors of infinite series and trigonometric Fourier series (Bor in Bull Sci Math 169:102990, 2021) by using almost increasing sequences. In this paper, we have generalized these theorems to \(|\bar{N},p_n;\theta _{n}|_{k}\) summability methods. Some new and known results are also obtained.
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On pseudo Z-symmetric Lorentzian manifolds admitting a type of semi-symmetric metric connection Anal. Math. Phys. (IF 1.7) Pub Date : 2023-10-19 Hülya Bağdatlı Yılmaz
The paper aims to investigate the general properties of pseudo Z-symmetric Lorentzian manifolds with semi-symmetric metric \( \rho \)-connection \( {\bar{\nabla }} \) and examine compatibility conditions. Moreover, such a manifold is applied to general relativity and its physical consequences are given.
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The balanced metrics and cscK metrics on polyball bundles Anal. Math. Phys. (IF 1.7) Pub Date : 2023-10-19 Zhiming Feng, Zhenhan Tu
In this paper, we use the the well-known Calabi ansatz, further generalized by Hwang–Singer and Apostolov–Calderbank–Gauduchon, to study the existence of constant scalar curvature Kähler (cscK for short) metrics and balanced metrics on certain holomorphic polyball bundles M which are locally expressed as \(M=\Big \{(z_1,\ldots ,z_{{\mathcal {N}}}, u_1,\ldots ,u_{\ell })\in \prod _{j=1}^{{\mathcal {N}}}\Omega
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Marcinkiewicz exponent and boundary value problems in fractal domains of $${\mathbb {R}}^{n+1}$$ Anal. Math. Phys. (IF 1.7) Pub Date : 2023-10-18 Carlos Daniel Tamayo Castro
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On the Dirichlet problem for the Schrödinger equation in the upper half-space Anal. Math. Phys. (IF 1.7) Pub Date : 2023-10-16 Bo Li, Tianjun Shen, Jian Tan, Aiting Wang
A well-known result of Stein-Weiss in 1971 said that a harmonic function, defined on the upper half-space, is the Poisson integral of a Lebesgue function if and only if it is also a Lebesgue function uniformly in the time variable. Under a metric measure space setting, we show that a solution to the elliptic equation with a non-negative potential, defined on the upper half-space, is in the essentially-bounded-Morrey
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On a Riemann–Hilbert problem for $$\Psi $$ -hyperholomorphic functions in $${\mathbb R}^m$$ Anal. Math. Phys. (IF 1.7) Pub Date : 2023-10-10 José Luis Serrano Ricardo, Ricardo Abreu Blaya, Jorge Sánchez Ortiz
The purpose of this paper is to solve a kind of Riemann–Hilbert problem for \(\Psi \)-hyperholomorphic functions, which are linked with the use of non-standard orthogonal basis of the Euclidean space \({\mathbb R}^m\). We approach this problem using the language of Clifford analysis for obtaining the explicit solution of the problem in a Jordan domain \(\Omega \subset {\mathbb R}^m\). Since our study
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On a sufficient condition for the existence of unconditional bases of reproducing kernels in Fock type spaces with nonradial weights Anal. Math. Phys. (IF 1.7) Pub Date : 2023-10-06 K. P. Isaev, A. V. Lutsenko, R. S. Yulmukhametov
We describe some Fock type spaces which possess unconditional bases of reproducing kernels, the spaces \(\mathcal F_{\varphi }\) of entire functions f such that \(fe^{-\varphi }\in L_2({\mathbb {C}})\), where \(\varphi \) is a subharmonic function, which may be nonradial.
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An extensive study on parameterized inequalities for conformable fractional integrals Anal. Math. Phys. (IF 1.7) Pub Date : 2023-10-01 Fatih Hezenci, Hüseyin Budak
This paper proves an equality for the case of differentiable convex functions including the conformable fractional integrals. By using this equality, we establish several parameterized inequalities with the help of the conformable fractional integrals. Several inequalities are obtained by taking advantage of the convexity, the Hölder inequality, and the power mean inequality. Furthermore, we present
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Upper bounds for the number of isolated critical points via the Thom–Milnor theorem Anal. Math. Phys. (IF 1.7) Pub Date : 2023-09-25 Vladimir Zolotov
We apply the Thom–Milnor theorem to obtain the upper bounds on the amount of isolated (1) critical points of a potential generated by several fixed point charges(Maxwell’s problem on point charges), (2) critical points of SINR, (3) critical points of a potential generated by several fixed Newtonian point masses augmented with a quadratic term, (4) central configurations in the n-body problem. In particular
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Existence and multiplicity results for a multiparameter quasilinear Schrödinger equation Anal. Math. Phys. (IF 1.7) Pub Date : 2023-09-19 Francisco Julio S. A. Corrêa, Gelson C. G. dos Santos, Leandro S. Tavares
This paper is devoted to the study of existence and multiplicity of solutions for a multiparameter quasilinear Schrödinger problem whose hypotheses allows us to consider semipositone and critical concave convex problems. The approach is based by combining explicitely constructions of sub-supersolutions and variational methods.
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Solving the inverse Sturm–Liouville problem with singular potential and with polynomials in the boundary conditions Anal. Math. Phys. (IF 1.7) Pub Date : 2023-09-16 Egor E. Chitorkin, Natalia P. Bondarenko
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Fourier method for the Neumann problem on a torus Anal. Math. Phys. (IF 1.7) Pub Date : 2023-09-14 Z. Ashtab, J. Morais, R. Michael Porter
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Non-standard Green energy problems in the complex plane Anal. Math. Phys. (IF 1.7) Pub Date : 2023-09-09 Abey López-García, Alexander Tovbis
We consider several non-standard discrete and continuous Green energy problems in the complex plane and study the asymptotic relations between their solutions. In the discrete setting, we consider two problems; one with variable particle positions (within a given compact set) and variable particle masses, the other one with variable masses but prescribed positions. The mass of a particle is allowed
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Discrete even Fourier–Weyl transforms of $$A_1 \times A_1$$ Anal. Math. Phys. (IF 1.7) Pub Date : 2023-09-07 Goce Chadzitaskos, Jiří Hrivnák, Jan Thiele
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Lattice sums for double periodic polyanalytic functions Anal. Math. Phys. (IF 1.7) Pub Date : 2023-09-02 Piotr Drygaś, Vladimir Mityushev
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Unbounded Hamiltonians generated by Parseval frames Anal. Math. Phys. (IF 1.7) Pub Date : 2023-09-02 F. Bagarello, S. Kużel
In Bagarello and Kużel (Acta Appl Math 171:4, 2021) Parseval frames were used to define bounded Hamiltonians, both in finite and in infinite dimesional Hilbert spaces. Here we continue this analysis, with a particular focus on the discrete spectrum of Hamiltonian operators constructed as a weighted infinite sum of rank one operators defined by some Parseval frame living in an infinite dimensional Hilbert
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Inverse nodal problems for perturbed spherical Schrödinger operators Anal. Math. Phys. (IF 1.7) Pub Date : 2023-08-17 Yu Liu, Guoliang Shi, Jun Yan, Jia Zhao
The inverse nodal problem for perturbed spherical Schrödinger operator defined on (0, 1) is studied. We prove that the potential on the whole interval can be uniquely determined in terms of a twin dense nodal subset known on the interior subinterval \((a,1),a \in (0,1).\) Especially, when \(a \in \left( \frac{1}{2},1\right) ,\) we need additional spectral information, which is associated with the derivatives
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Zalcman’s problem and related two-radii theorems Anal. Math. Phys. (IF 1.7) Pub Date : 2023-08-03 Valery Volchkov, Vitaly Volchkov
Let G be the group of conformal automorphisms of the unit disc \({\mathbb {D}}=\{z\in {\mathbb {C}}:|z|<1\}\). For \(r>0\), we put \(B_{r}=\{z\in {\mathbb {D}}:|z|<\tanh r\}\). Denote by \(\overline{B}_{r}\) the closure of the disc \(B_r\), and by \(\partial B_{r}\) its boundary. Let \(\chi _r\) be the characteristic function (indicator) of \(B_r\). Assume that \(r_1, r_2\in (0,+\infty )\) are fixed
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Singular values inequalities via matrix monotone functions Anal. Math. Phys. (IF 1.7) Pub Date : 2023-07-30 Hamid Reza Moradi, Wasim Audeh, Mohammad Sababheh
This paper uses matrix monotone functions as a key tool to obtain several relations among the singular values of certain celebrated matrix quantities. This includes, but is not limited to, relations among the blocks of a block matrix, relations about the singular values of the matrix Heinz means, and some related matrix combinations. Our results improve some celebrated results from the literature.
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Boundedness of fractional heat semigroups generated by degenerate Schrödinger operators Anal. Math. Phys. (IF 1.7) Pub Date : 2023-07-29 Zhiyong Wang, Pengtao Li, Yu Liu
Let \(L=-\frac{1}{\omega }\textrm{div}(A(x)\cdot \nabla )+V\) be a degenerate Schrödinger operator in \({\mathbb {R}}^{n}\), where \(\omega \) is a weight of the Muckenhoupt class \(A_{2}\), A(x) is a real and symmetric matrix depending on x and satisfies $$\begin{aligned} C^{-1}\omega (x)|\xi |^{2} \le A(x)\xi _{i}\overline{\xi _{j}}\le C\omega (x)|\xi |^{2} \end{aligned}$$ for some positive constant
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Transcendental solutions of Fermat-type functional equations in $$ \mathbb {C}^n $$ Anal. Math. Phys. (IF 1.7) Pub Date : 2023-07-25 Molla Basir Ahamed, Vasudevarao Allu
The equation \(f^n+g^n=1\) can be interpreted as the Fermat Diophantine equation \(x^n+y^n=1\) within the function field when n is a positive integer. This study employs Nevanlinna theory for several complex variables to explore transcendental solutions of Fermat-type functional equations with polynomial coefficients in \(\mathbb {C}^n\). If the coefficients of the equation are transcendental functions
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On Bergman kernel functions and weak holomorphic Morse inequalities Anal. Math. Phys. (IF 1.7) Pub Date : 2023-07-20 Xiaoshan Li, Guokuan Shao, Huan Wang
We give simple and unified proofs of weak holomorhpic Morse inequalities on complete manifolds, q-convex manifolds, pseudoconvex domains, weakly 1-complete manifolds and covering manifolds. This paper is essentially based on the asymptotics of Bergman kernel functions and the Bochner–Kodaira–Nakano formulas.
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Strongly singular Calderón–Zygmund operators on Hardy spaces associated with ball quasi-Banach function spaces Anal. Math. Phys. (IF 1.7) Pub Date : 2023-07-18 Kwok-Pun Ho
We obtain the mapping properties of the strongly singular Calderón–Zygmund operators on Hardy spaces associated with ball quasi-Banach function spaces. We established this result by using the idea from extrapolation originated from Rubio de Francia. As applications of this result, we present the mapping properties of the strongly singular Calderón–Zygmund operators to the Hardy Orlicz-slice spaces
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Normalization of strongly hyperbolic logarithmic transseries and complex Dulac germs Anal. Math. Phys. (IF 1.7) Pub Date : 2023-07-06 Dino Peran
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On quantum star graphs with eigenparameter dependent vertex conditions Anal. Math. Phys. (IF 1.7) Pub Date : 2023-07-05 Gökhan Mutlu, Ekin Uğurlu
We investigate the spectral properties of two different boundary value problems on a compact star graph in which the vertex conditions are dependent on the spectral parameter. We treat these boundary value problems as eigenvalue problems in some extended Hilbert spaces by associating them with vector-valued operators. We prove that the corresponding operators are self-adjoint. We construct the characteristic
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A geometric construction of isospectral magnetic graphs Anal. Math. Phys. (IF 1.7) Pub Date : 2023-07-05 John Stewart Fabila-Carrasco, Fernando Lledó, Olaf Post