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Herein, the Laplace transform representations for functions of weighted holomorphic Bergman spaces on the tube domains are developed. Then a weighted version of the edge-of-the-wedge theorem is derived as a byproduct of the main results. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the L p regularity of weighted Bergman projection on the unit ball B n and complex space C n with radial weight. We prove that the weighted Bergman projection on L p (B n , ρ 1) and L p (C n , ρ 2) is bounded only if p = 2 , respectively, where ρ 1 (z) = (1 − | z | 2 ) A 1 exp ⁡ { − B 1 (1 − | z | 2 ) α 1 } and ρ 2 (z) = | z | 2 A 2 e − B 2 | z | 2 α 2 . [ABSTRACT FROM AUTHOR]

In this paper, we investigate the growth and fixed points of solutions of higher-order linear differential equations in the unit disc. We extend the coefficient conditions to a type of one-constant-control coefficient comparison and obtain the same estimates of iterated order of solutions. We also obtain better estimates by providing a precise value of iterated order of solution instead of a range of that in the case of coefficient characteristic function comparison. Moreover, we utilize iteration to investigate and estimate the fixed points of solutions' arbitrary-order derivatives with higher-order equations f (k) + A k − 1 (z) f (k − 1) + ⋯ + A 1 (z) f ′ + A 0 (z) f = 0 and provide a concise method to judge if the items generated by the iteration do not vanish identically and ensure the iteration proceeds. Our results are an improvement over those by B. Belaïdi, T. B. Cao, G. W. Zhang and A. Chen. [ABSTRACT FROM AUTHOR]

This paper aims to obtain decompositions of higher dimensional functions into sums of non-tangential boundary limits of the corresponding Hardy space functions on tubes for the index range . In the one-dimensional case, Deng and Qian recently obtained such a Hardy space decomposition result: for any function , there exist functions and such that , where and are, respectively, the non-tangential boundary limits of some Hardy space functions in the upper-half and lower-half planes. In the present paper, we generalize the one-dimensional Hardy space decomposition result to the higher dimensions and discuss the uniqueness issue of such decomposition. [ABSTRACT FROM AUTHOR]

In this paper we consider Hardy space decomposition ofwherestands for the open unit disc, andis its boundary. Hardy spaces decompositions forandforare, as classical results, available in the literature. Forthe basic tools are the Plemelj formula and the boundedness of the Hilbert transformation. Forneither on the real line, nor on the unit circle, a Plemelj formula, or Hilbert transformation are available. In a recent paper Deng and Qian obtain Hardy spaces decomposition foron the real line by means of rational approximation. In the present paper by using rational functions, we achieve the same goal forfor the rangeThe work on the unit circle exposes the particular features of the kind of decomposition in the compact situation adaptable to higher dimensions. [ABSTRACT FROM AUTHOR]

In this article, motivated by the classic Hadamard factorization theorem about an entire function of finite order in the complex plane, we firstly prove that a harmonic function whose positive part satisfies some growth conditions, can be represented by its integral on the boundary of the half space. By using Nevanlinna's representation of harmonic functions and the modified Poisson kernel of the half space, we further prove a representation formula through integration against a certain measure on the boundary hyperplane for harmonic functions not necessarily continuous on the boundary hyperplane whose positive parts satisfy weaker growing conditions than the first question. The result is further generalized by involving a parameter m dealing with the singularity at the infinity. [ABSTRACT FROM AUTHOR]

In this article, we first give the asymptotic behaviors of fractional Laplacians in the half space of R n . Next, we discuss the weighted boundary limits of modified fractional Laplacians. The asymptotic behaviors hold outside an explicitly defined exceptional set, whose size can be controlled and set to be as small as required. The estimation of the asymptotic behavior is the generalization of the argument reported in Qiao and Deng (2010). [ABSTRACT FROM AUTHOR]

Abstract: The work strengthens the result established by L. Cohen on uncertainty principle involving phase derivative. We propose stronger uncertainty principles not only in the classical setting for Fourier transform, but also for self-adjoint operators. We also deduce the conditions that give rise to the equal relation of the uncertainty principle. Examples are provided to show that the new uncertainty principle is truly sharper than the existing ones in literature. [Copyright &y& Elsevier]

This study devotes to uncertainty principles under the linear canonical transform (LCT) of a complex signal. A lower-bound for the uncertainty product of a signal in the two LCT domains is proposed that is sharper than those in the existing literature. We also deduce the conditions that give rise to the equal relation of the new uncertainty principle. The uncertainty principle for the fractional Fourier transform is a particular case of the general result for LCT. Examples, including simulations, are provided to show that the new uncertainty principle is truly sharper than the latest one in the literature, and illustrate when the new and old lower bounds are the same and when different. [ABSTRACT FROM AUTHOR]

LetApdenote the class of analytic andp-valent functions in the open unit discU={z:|z|<1}. Putand definein terms of the Hadmard product (or convolution)In this paper, we introduce certain new subclasses of spiral-like multivalent functions defined by using the operatorand investigate several inclusion properties of these classes. Also, some applications involving integral operator are considered. [ABSTRACT FROM AUTHOR]

In this article, a solution of the Dirichlet problem for the Schrödinger operator on a cone is constructed by the generalized Poisson integral with a slowly growing continuous boundary function. A solution of the Poisson integral for any continuous boundary function is also given explicitly by the Poisson integral with the generalized Poisson kernel depending on this boundary function. MSC: 31B05, 31B10. [ABSTRACT FROM AUTHOR]

Abstract: Analytic signals of finite energy in signal analysis are identical with non-tangential boundary limits of functions in the related Hardy spaces. With this identification this paper studies a subclass of the analytic signals that, with the amplitude-phase representation , , satisfy the relation a.e., signals in this subclass are called mono-components, and, in that case, the phase derivative is called the analytic instantaneous frequency of s. This paper proves that when , where is real-valued, band-limited with minimal bandwidth B and is real-valued, as the restriction on the real line of some entire function, then s is an analytic signal if and only if is a linear function, and with there holds . In the case s is a mono-component. This generalizes the corresponding result obtained by Xia and Cohen in 1999 in which is assumed to be a real-valued polynomial. [Copyright &y& Elsevier]

The Dirac- δ distribution may be realized through sequences of convolutions, the latter being also regarded as approximation to the identity. This paper proposes the real form of pre-orthogonal adaptive Fourier decomposition (POAFD) method to realize fast approximation to the identity. It belongs to sparse representation of signals having potential applications in signal and image analysis. [ABSTRACT FROM AUTHOR]

Herein, a weighted version of the Paley–Wiener-type theorem for analytic functions in a tubular domain over a regular cone is obtained by using H p space methods. Then, the classical n -dimensional Paley–Wiener theorem is generalized to a case wherein 0 < p < 2. Finally, a version of the edge-of-the-wedge theorem is obtained as an application of the weighted theorems. [ABSTRACT FROM AUTHOR]

In this paper we first prove the existence of the n -best approximation in terms of the parameterized Szegö kernels in the stochastic complex Hardy space of the unit disc. It is a generalization to random signals of the corresponding result for the Hardy space of the disc, and has applications in signal analysis. The result may be generalized to the randomized polydisc case with potential applications in image processing. A practical algorithm for the approximation is proposed. [ABSTRACT FROM AUTHOR]

We generalize Matsaev’s theorem for subharmonic functions from two to higher dimension. The proofs are nontrivial and constructive. [ABSTRACT FROM PUBLISHER]

In this paper, we prove that if the positive part u+(x) of a harmonic function u(x) in the upper half space satisfies a fast growing condition, then its negative part u-(x) can also be dominated by a similar growing condition. Meanwhile, u(x) can be represented in terms of the modified Poisson integral and a harmonic function vanishing on the boundary. [ABSTRACT FROM AUTHOR]

The object of this paper was to study two majorization results for the subclasses S s ∗ and S c ∗ of starlike functions, which are, respectively, associated with the sine and cosine functions, without acting upon any linear or nonlinear operators to the above function classes. [ABSTRACT FROM AUTHOR]

Very recently, Tang et al [ABSTRACT FROM AUTHOR]