样式: 排序: IF: - GO 导出 标记为已读
-
Truncated Second Main Theorem for Holomorphic Curves on Annuli with Moving Hyperplanes Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-15 Nhung Thi Nguyen, An Van Nguyen
In this paper, we establish some truncated second main theorems for holomorphic curve from an annulus into \({\mathbb {P}}^n({\mathbb {C}})\) and moving hyperplanes. We also use these results to solve unique problems with moving targets.
-
Hardy Type Theorems for Linear Canonical Dunkl Transform Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-13 Ahmed Saoudi
In this paper, we establish an analogue of Hardy’s theorems for the linear canonical Dunkl transform and fractional Dunkl transform, which generalizes a large class of a family of integral transforms. As application, we derive Hardy type theorems for fractional Hankel type transform, one dimension Dunkl Fresnel transform, linear canonical transform and fractional Fourier transform.
-
Complex Symmetry of Linear Combinations of Composition Operators on the McCarthy–Bergman Space of Dirichlet Series Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-12 Cheng-shi Huang, Zhi-jie Jiang
-
On the Resolvent Matrix of the Truncated Hausdorff Matrix Moment Problem Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-11
Abstract We obtain the resolvent matrix of the truncated Hausdorff matrix moment (THMM) problem on the interval [a, b] in case of an even and odd number of moments expressed in terms of terminal point b. An explicit relation between the resolvent matrices of the THMM problem with respect to terminal points a and b is presented.
-
Two q-Operational Equations and Hahn Polynomials Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-10
Abstract Motivated by Liu’s (Sci China Math 66:1199–1216, 2023) recent work. This article reveals the essential features of Hahn polynomials by presenting a new q-exponential operator, that is $$\begin{aligned} \exp _q(t\Delta _{x,a})f(x)=\frac{(axt;q)_{\infty }}{(xt;q)_{\infty }} \sum _{n=0}^{\infty }\frac{t^n}{(q;q)_n} f(q^n x) \end{aligned}$$ with \(\Delta _{x,a}=x (1-a)\eta _a+\eta _x\) and \(\eta
-
Approximation by Meromorphic k-Differentials on Compact Riemann Surfaces Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-10 Nadya Askaripour
The main theorem of this article is a Runge type theorem proved for k-differentials \((k\ge 2)\). The integrability in the \(L^1\)- norm is defined for k-differentials in Section 2. We consider k-differentials which are integrable in the defined \(L^1\)- norm on the Riemann surface, and are holomorphic on an open subset of that surface. We will show those k-differentials can be approximated by meromorphic
-
On Decomposition for Pairs of Twisted Contractions Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-10
Abstract This paper presents Wold-type decomposition for various pairs of twisted contractions on Hilbert spaces. We achieve an explicit decomposition for pairs of twisted contractions such that the c.n.u. parts of the contractions are in \(C_{00}\) . The structure for pairs of doubly twisted operators consisting of a power partial isometry has been discussed. It is also shown that for a pair \((T
-
Fredholm Index of 3-Tuple of Restriction Operators and the Pair of Fringe Operators for Submodules in $$H^2({\mathbb {D}}^3)$$ Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-09 Xilin Nie, Anjian Xu
For a submodule \({\mathcal {M}}\) in Hardy module \(H^2({\mathbb {D}}^n)\) on the unit polydisc in \(\mathbb {C}^{n}\), we define the \(n-1\) tuple of fringe operators \(\textbf{F}=(F_{1},F_{2},\ldots ,F_{n-1})\) and the n tuple of restriction operators \(\textbf{R}=(R_{z_{1}},R_{z_{2}},\ldots , R_{z_{n}})\) with respect to \({\mathcal {M}}\). In this paper, for the case \(n=3\), it is shown that
-
Least Energy Sign-Changing Solution for N-Kirchhoff Problems with Logarithmic and Exponential Nonlinearities Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-08 Ting Huang, Yan-Ying Shang
In this paper, we are concerned with the existence of least energy sign-changing solutions for the following N-Laplacian Kirchhoff-type problem with logarithmic and exponential nonlinearities: $$\begin{aligned} \left\{ \begin{array}{ll} -\left( a+b \int _{\Omega }|\nabla u|^{N} d x\right) \Delta _{N} u=|u|^{p-2} u \ln |u|^{2}+\lambda f(u), &{} \text{ in } \Omega , \\ u=0, &{} \text{ on } \partial \Omega
-
Abstract Algebraic Construction in Fractional Calculus: Parametrised Families with Semigroup Properties Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-08 Arran Fernandez
What structure can be placed on the burgeoning field of fractional calculus with assorted kernel functions? This question has been addressed by the introduction of various general kernels, none of which has both a fractional order parameter and a clear inversion relation. Here, we use ideas from abstract algebra to construct families of fractional integral and derivative operators, parametrised by
-
On a Class of Subdiagonal Algebras Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-04
Abstract We investigate some new classes of operator algebras which we call semi- \(\sigma \) -finite subdiagonal and Riesz approximable. These constitute the most general setting to date for a noncommutative Hardy space theory based on Arveson’s subdiagonal algebras. We develop this theory and study the properties of these new classes.
-
On Perturbation of Operators and Rayleigh-Schrödinger Coefficients Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-04 Marcus Carlsson, Olof Rubin
Let A and E be self-adjoint matrices or operators on \(\ell ^2({{\mathbb {N}}})\), where A is fixed and E is a small perturbation. We study how the eigenvalues of \(A+E\) depend on E, with the aim of obtaining second order formulas that are explicitly computable in terms of the spectral decomposition of A and a certain block decomposition of E. In particular we extend the classical Rayleigh-Schrödinger
-
Boas Type Results for Two-Sided Quaternion Fourier Transform and Uniform Lipschitz Spaces Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-04
Abstract For the quaternion algebra \({\mathbb {H}}\) and \(f:\mathbb R^2\rightarrow {\mathbb {H}}\) , we consider a two-sided quaternion Fourier transform \(\widehat{f}\) . Necessary and sufficient conditions for f to belong to generalized uniform Lipschitz spaces are given in terms of behavior of \(\widehat{f}\) .
-
On the Toeplitz Algebra in the Case of All Entire Functions and All Functions Holomorphic in the Unit Disc Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-02 M. Jasiczak
We study the algebra generated by all Toeplitz operators on the Fréchet space of all entire functions and all functions holomorphic in the unit disk. In both cases we prove that the quotient algebra by the commutator ideal can be equipped with a locally convex topology which makes this quotient algebra algebraically and topologically isomorphic with the symbol algebra. We also show that the topology
-
Fractional Integration on Mixed Norm Spaces. I Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-02 Feng Guo, Xiang Fang, Shengzhao Hou, Xiaolin Zhu
In this paper we characterize completely the septuple $$\begin{aligned} (p_1, p_2, q_1, q_2; \alpha _1, \alpha _2; t) \in (0, \infty ]^4 \times (0, \infty )^2 \times {\mathbb {C}} \end{aligned}$$ such that the fractional integration operator \({\mathfrak {I}}_t\), of order \(t \in {\mathbb {C}}\), is bounded between two mixed norm spaces: $$\begin{aligned} {\mathfrak {I}}_t: H(p_1, q_1, \alpha _1)
-
Variational Principles in Quaternionic Analysis with Applications to the Stationary MHD Equations Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-01 P. Cerejeiras, U. Kähler, R. S. Kraußhar
In this paper we aim to combine tools from variational calculus with modern techniques from quaternionic analysis that involve Dirac type operators and related hypercomplex integral operators. The aim is to develop new methods for showing geometry independent explicit global existence and uniqueness criteria as well as new computational methods with special focus to the stationary incompressible viscous
-
Higgs Algebras in Classical Harmonic Analysis Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-03-01 David Eelbode
In this paper, we will prove that the reproducing kernels \(Z_k({\underline{x}},{\underline{u}})\) for the spaces \({\mathcal {H}}_k({\mathbb {R}}^m,{\mathbb {C}})\) of k-homogeneous harmonics can be seen as elements of an infinite-dimensional ladder operator representation for a cubic polynomial angular momentum algebra which is known as the Higgs algebra. This algebra will be shown to be one of two
-
$$\varepsilon $$ -Numerical Range of Operator Polynomial Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-02-23 Kamel Mahfoudhi
Relying on some ideas of numerical ranges, we introduce, for operators polynomials on a complex Hilbert space, a new notion called the \(\varepsilon \)-numerical range of operators polynomials. Some geometrical and topological properties of these \(\varepsilon \)-numerical range are proved. Thereby, we achieve a new characterization of \(\varepsilon \)-numerical range of operators polynomials on an
-
Harmonic Bergman Spaces on the Real Hyperbolic Ball: Atomic Decomposition, Interpolation and Inclusion Relations Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-02-22 A. Ersin Üreyen
For \(\alpha >-1\) and \(0
-
Non-tangential Limits and Bounded Point Derivations on $$R^2(X)$$ Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-02-21 Stephen Deterding
We study \(L^2\) approximations of rational functions on the complex plane, focusing on bounded point derivations. We show that if there is a bounded point derivation at x and \(\{x_n\}\) is a sequence of points that converges non-tangentially to x, then the sequence of derivatives \(\{f^{\prime }(x_n)\}\) is uniformly bounded for a large class of functions, specifically those functions which can be
-
Hankel Operators Between Different Fock–Sobolev Type Spaces Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-02-19 Jianjun Chen, Xiaofeng Wang, Jin Xia, Guangxia Xu
In this paper, we study Hankel operators on the Fock–Sobolev type spaces for all possible \(1\le p,q<\infty \) and \(\alpha \in {\mathbb {R}}\). We introduce a function space called integrable mean oscillation on \({\mathbb {C}}^n\). Then we characterize those symbols f for which the Hankel operators \(H^\alpha _f\) and \(H^\alpha _{{{\bar{f}}}}\) are simultaneously bounded (or compact) from Fock–Sobolev
-
Hadamard–Bergman Operators on Weighted Spaces Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-02-16 Alexey Karapetyants, Adolf Mirotin, Evelin Morales
This article continues the study of the Hadamard–Bergman operators in the unit disc of the complex plane. These operators arose as a natural generalization of the orthogonal projector and represent an integral realization of multiplier operators. Here we consider mainly the further development of the theory of such operators in the context of operators of variable order, that is, with kernels depending
-
Generalized Convolution Operator Associated with the (k, a)-Generalized Fourier Transform on the Real Line and Applications Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-02-12 Hatem Mejjaoli
-
Steven George Krantz (1951 -) Celebrates his 70th Birthday Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-02-08 Arni S. R. Srinivasa Rao, Siqi Fu, Gregory Knese, Kaushal Verma, Brett Wick
-
Fredholm and Frame-Preserving Weighted Composition Operators Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-02-07 Jasbir Singh Manhas, Ruhan Zhao
We characterize Fredholm and frame-preserving weighted composition operators on some general Hilbert spaces of holomorphic functions in bounded domains in \({\mathbb {C}}^n\).
-
A Class of Norm Inequalities for Operator Monotone Functions and Hyponormal Operators Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-02-06 Katarina Bogdanović
-
Difference of Weighted Composition Operators Over the Ball Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-02-06 Boo Rim Choe, Koeun Choi, Hyungwoon Koo, Inyoung Park
Recently, Choe et al. obtained characterizations for bounded/compact differences of weighted composition operators acting from a standard weighted Bergman space into another over the unit disk. In this paper we extend those results to the ball setting. By devising a new approach regarding test functions, we improve the characterizations as well as the proofs. Namely, the Reproducing Kernel Thesis is
-
Property $$\mathcal {P}$$ and Compact Perturbations Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-01-31 Ting Ting Zhou, Li Qi Xiu
Let \(\mathcal {H}\) be a complex separable infinite dimensional Hilbert space. An operator T acting on \(\mathcal {H}\) is said to have property \(\mathcal {P}\), if \(\sigma (T)=\sigma _p(T)\) and \(\sigma (T^*)=\sigma _p(T^*)\). In this paper, we characterize those operators which have an arbitrarily small compact perturbation to satisfy property \(\mathcal {P}\). Also, we study the stability of
-
The Bicomplex Dual Fractional Hankel Transform Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-01-29 Adam Hammam
We provide a concrete characterization of the Bergman space of bicomplex-valued bc-meromorphic functions with a strong pole at the origin of the bicomplex discus. The explicit expression of its reproducing kernel is given, and its integral representation as the range of the bicomplex version of the generalized second Bargmann transform is also considered. In addition, we construct the bicomplex analog
-
Stability Estimates in Determination of Non-orientable Surface from Its Dirichlet-to-Neumann Map Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-01-27
Abstract Let (M, g) and \((M',g')\) be non-orientable Riemannian surfaces with fixed boundary \(\Gamma \) and fixed Euler characterictic m, and \(\Lambda \) and \(\Lambda '\) be their Dirichlet-to-Neumann maps, respectively. We prove that the closeness of \(\Lambda '\) to \(\Lambda \) in the operator norm implies the existence of the near-conformal diffeomorphism \(\beta \) between (M, g) and \((M'
-
Normal Holomorphic Mappings in Complex Space Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-01-24 Peter V. Dovbush, Steven G. Krantz
We study normal holomorphic mappings on complex spaces and complex manifolds. Applications are provided.
-
Free Probability on Banach Algebras Induced by Scaled Hypercomplex Numbers Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-01-23 Ilwoo Cho
In this paper, we construct certain multiplicative algebraic structure \({{\mathcal {G}}}_{t}\), and the corresponding Banach algebra \({{\mathscr {M}}}_{t}\) generated by \({{\mathscr {G}}}_{t}\) over the complex field \({{\mathbb {C}}}\), where \({{\mathscr {G}}}_{t}\) is induced by the \({{\mathbb {R}}}\)-algebra \({{\mathbb {H}}}_{t}\) of all t-scaled hypercomplex numbers, for \(t\in {{\mathbb
-
Existence of Solutions for a Singular Double Phase Kirchhoff Type Problems Involving the Fractional q(x, .)-Laplacian Operator Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-01-18 Rym Chammem, Abdeljabbar Ghanmi, Mahfoudh Mechergui
In this paper, we consider a class of fractional Laplacian problems involving fractional \(q_{i}(x)\)-laplacian operators \( (i=1:2)\), and a singular nonlinearity. By using variational methods and monotonicity arguments combined with the theory of the generalized Lebesgue Sobolev spaces, we prove the existence of solutions for such problems. An illustrative example is presented to validate the main
-
Existence of Multiple Solution for a Singular p(x)-Laplacian Problem Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-01-18 A. Ghanmi, L. Mbarki, Debajyoti Choudhuri
We will study the following singular problem $$\begin{aligned} \left\{ \begin{array}{ll} -div(|\nabla \varphi |^{p(x)-2}\nabla \varphi )+\Psi (x)|\varphi |^{p(x)-2}\varphi = a(x)\varphi ^{-\gamma (x)}+\lambda f(x,\varphi ),\quad \text{ in } \Omega , \\ \\ \varphi =0, \quad \text{ on } \partial \Omega . \end{array} \right. \end{aligned}$$ Here \(\Omega \subset \mathbb {R}^N, (N> 2)\) is a bounded domain
-
Fourier Kernels Associated with the Clifford–Helmholtz System Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-01-17
Abstract In this paper we present a family of solutions of the Clifford–Helmholtz system, which factors the standard Helmholtz equation. All these solutions can be used as integral kernels of generalized Fourier transforms in hypercomplex analysis. We show that in the Laplace domain they have interesting expressions in terms of terminating hypergeometric functions. This allows us to compute recursion
-
Catalan Numbers and Free Distributions of Mutually Free Multi Semicircular Elements Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-01-09 Ilwoo Cho, Junyi Dong
In this paper, we consider certain relations among Catalan numbers, and study free distributions of mutually free, multi semicircular elements. We not only characterize the joint free distributions of given multi semicircular elements, but also provide estimations for such free-distributional data by using our relations among Catalan numbers. As application, asymptotic behaviors of the joint free distribution
-
On a New Characterization of the True-Poly-Analytic Bargmann Spaces Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-01-08 Abdelhadi Benahmadi, Allal Ghanmi
We consider a novel bounded integral transform with a kernel function being the n-th polyanalytic Intissar–Hermite polynomial. We provide a concrete description of its range, shown to be a reproducing kernel Hilbert space for which we provide an explicit closed formula of its reproducing kernel. The limit of these ranges leads, in a precise sense, to the so-called van Eijndhoven–Meyers Bargmann space
-
Three-Jets Determinations of Normalized Proper Holomorphic Maps from $$ \mathbb {H}_n$$ into $$\mathbb {H}_{3n-2}$$ Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-01-02 Nuray Gul, Shanyu Ji, Wanke Yin
We derive the explicit formula for the normalized rational proper holomorphic maps of \(Rat({\mathbb H}_n, {\mathbb H}_{3n-2})\). As a consequence, we prove that these maps are determined by their three jets.
-
Stochastic Clairaut Equation on Algebra of Generalized Functions Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-01-03 Hafedh Rguigui
Based on an infinite dimensional distributions space, we study the solution of the generalized stochastic Clairaut equation using a suitable convolution calculus. The solution of such equation is shown to be positive and its integral representation with respect to the Radon measure is given. Moreover, the contractivity property is studied. Finally, the system is shown to be finite-time stochastically
-
On the Matrix q-Kummer Equation and Its Solutions Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-01-03 Ravi Dwivedi
In the present paper, a general theory for the second-order matrix difference equation of bilateral type is discussed. We introduced the matrix q-Kummer equation of bilateral type and presented the q-Kummer matrix function as a series solution. Later, we obtain the integral solutions of this Kummer equation and solution at \(\infty \). We also give a brief idea about the matrix Gauss difference equation
-
Holomorphic Functions on the Lie Ball and Their Monogenic Counterparts Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-01-05 Brian Jefferies
The Cauchy integral formula in Clifford analysis allows us to associate a holomorphic function \({\tilde{f}}:L_n\rightarrow {\mathbb C}\) on the Lie ball \(L_n\) in \({\mathbb C}^n\) with its monogenic counterpart \(f:B_1(0)\rightarrow {\mathbb C}^{n+1}\) via the formula \({\tilde{f}}(z) = \int _{S^n}G_{\omega }(z){\varvec{n}}({\omega })f({\omega })\,d\mu ({\omega })\), \(z\in L_n\). The inverse map
-
Discrete Weierstrass Transform: Generalisations Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2024-01-05 A. Massé, H. De Ridder
-
Quaternion Hyperbolic Fourier Transforms and Uncertainty Principles Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2023-12-29 M. Ferreira, J. Morais
-
On an Interpolation Problem for the Classical Weighted Harmonic Bergman Space Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2023-12-12 Mohammed El Aïdi
We provide sufficient conditions for interpolating a sequence by a function belonging to the classical weighted harmonic Bergman space defined on the unit real ball.
-
Weak-Type Regularity of the Bergman Projection on n-Dimensional Hartogs Triangles Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2023-12-12 Yuanyuan Jing, Yi Li, Chuan Qin, Mengjiao Wang
In this paper, we research the weak-type regularity of the Bergman projection for n-dimensional generalized Hartogs triangles. The weak-type regularity of the Bergman projection of 2-dimensional Hartogs triangles and the rational power-generalized 2-dimensional Hartogs triangles has been studied by Huo-Wick and Christopherson-Koenig, respectively. Motivated by their works, we show that, for generalized
-
Free Probability on the Limit $$C^{*}$$ -Algebra Induced by a Chain of Graphs Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2023-12-08 Ilwoo Cho, Palle E. T. Jorgensen
In this paper, we consider the limit \(C^{*}\)-algebra induced by a chain of connected finite directed graphs, and study the free probability on it. In particular, we are interested in semicircular elements in the limit \(C^{*}\)-algebra whose free distributions are the semicircular law. Our main results not only characterize free-distributional data on the limit \(C^{*}\)-algebra, but also provide
-
Cauchy Formulae and Hardy Spaces in Discrete Octonionic Analysis Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2023-12-09 Rolf Sören Kraußhar, Dmitrii Legatiuk
In this paper, we continue the development of a fundament of discrete octonionic analysis that is associated to the discrete first order Cauchy–Riemann operator acting on octonions. In particular, we establish a discrete octonionic version of the Borel–Pompeiu formula and of Cauchy’s integral formula. The latter then is exploited to introduce a discrete monogenic octonionic Cauchy transform. This tool
-
Nonlinear Riemann-Hilbert Problems for Axial- and Bi-axial-monogenic Functions Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2023-12-08 M. Almeida, P. Cerejeiras, U. Kähler
In this paper we show a new approach to study Riemann-Hilbert (RH) problems in the context of monogenic functions over axial- and bi-axial domains. The basic idea is to reduce the problem to a RH problem for a complex Vekua system. This approach allows us not only to study classic linear, but also nonlinear RH problems, thus providing an important step towards the study of the general case of nonlinear
-
Fundamental Solutions for the Laplace–Beltrami Operator Defined by the Conformal Hyperbolic Metric and Jacobi Polynomials Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2023-12-08 Sirkka-Liisa Eriksson, Heikki Orelma
In this paper we study fundamental solutions for the Laplace–Beltrami operator $$\begin{aligned} \Delta _\alpha f=x_n^{\frac{\alpha }{n-2}}\Big (\Delta f-\frac{\alpha }{x_n}\frac{\partial f}{\partial x_n}\Big ), \end{aligned}$$ defined on smooth enough functions in \(\mathbb {R}_+^{n}=\{ (x_1,\ldots ,x_n)\in \mathbb {R}^{n}: x_n>0\}\). We represent explicit formulas for the fundamental solutions. Moreover
-
Polar Decomposition and Functional Calculus for Generalized Tomita’s Observables Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2023-12-07 Hiroshi Inoue, Camillo Trapani
Continuing previous studies by one of us (HI), a polar decomposition and a functional calculus for an unbounded Tomita’s observable are studied. For both problems we distinguish two different cases dictated by commutation properties.
-
Density of Complex and Quaternionic Polyanalytic Polynomials in Polyanalytic Fock Spaces Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2023-12-06 Sorin G. Gal, Irene Sabadini
In this paper we consider the polyanalytic Fock spaces both in the complex and in the quaternionic case. In this latter case, the polyanalytic functions are considered in the slice regular case, and we shall treat Fock spaces of the first and of the second kind. In all these spaces we prove quantitative results in the approximation by polyanalytic polynomials. The quantitative approximation results
-
Sharp Coefficients Bounds for Starlike Functions Associated with Gregory Coefficients Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2023-12-04 Sercan Kazımoğlu, Erhan Deniz, H. M. Srivastava
-
Spectral Approximation of Generalized Schrödinger Operators via Approximation of Subwords Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2023-12-04 Fabian Gabel, Dennis Gallaun, Julian Grossmann, Marko Lindner, Riko Ukena
-
Compact Bergman Type Operators Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2023-11-28 Lijia Ding
We characterize the \(L^p\)–\(L^q\) compactness of Bergman type operators, which are singular integral operators induced by the modified Bergman kernel on the complex unit ball. Moreover, we characterize Schatten class and Macaev class Bergman type integral operators on the Lebesgue space and the Bergman space by the methods of spectral estimates and operator inequalities; we also give a relatively
-
On the Convergence of Bernstein-Kantorovich-Stancu Shifted Knots Operators involving Schurer Parameter Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2023-11-27 Abdullah Alotaibi, Md. Nasiruzzaman, S. A. Mohiuddine
In the present article we want to study the convergence and other related properties of Schurer type Bernstein–Kantorovich–Stancu operators with Shifted knots. First we design the Bernstein–Kantorovich operators of the of Stancu type polynomials by Shifted knots of real parameters by including the Schurer positive real parameters, then obtain the convergence properties in terms of the continuous function
-
Modulus of Smoothness and Approximation Theorems in Clifford Analysis Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2023-11-21 Othman Tyr
This paper uses some basic results on Clifford analysis introduced by E. Hitzer, to study some problems in the theory of approximation of functions in the space of square integral functions in the Clifford algebra. The equivalence between the moduli of smoothness of all orders constructed by the Steklov function and the K-functionals constructed from the Sobolev-type space is proved. A consequence
-
Some New Characterizations of a Hermitian Matrix and Their Applications Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2023-11-17 Yongge Tian
A square matrix A over the field of complex numbers is said to be Hermitian if \(A = A^{*}\), the conjugate transpose of A, while Hermitian matrices are known to be an important class of matrices. In addition to the definition, a Hermitian matrix can be characterized by some other matrix equalities. This fact can be described in the implication form \(f(A, A^{*}) = 0 \Leftrightarrow A = A^{*}\), where
-
Stochastic Ditichlet–Poisson Problem on Hilbert Spaces Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2023-11-14 Sonia Chaari, Afef Ben Farah
This paper is devoted to the study of the existence and the uniqueness of the solution of the Stochastic Dirichlet-Poisson problems on Hilbert spaces. We prove that the unique solution of this equation is given by a probabilistic formula.
-
An Overview of the Exterior Matrix Method Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2023-11-08 William Paulsen
-
Generalized Weighted Composition Operators on Vector-Valued Weighted Bergman Space Complex Anal. Oper. Theory (IF 0.8) Pub Date : 2023-11-07 Anuradha Gupta, Geeta Yadav
In this research article the necessary and sufficient conditions for the norm of composition operator \(C_{\Phi }\) on \({\mathcal {A}}_{\alpha }^2(H)\) to be one are obtained. Moreover, \(C_{\Phi }\) is unitary on \({\mathcal {A}}_{\alpha }^2(H)\) if and only if it is co-isometry. The necessary and sufficient condition for Hermitian and normal composition operators on \({\mathcal {A}}_{\alpha }^2(H)\)