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In this review article we present regularity properties of generalized functions which are useful in the analysis of non-linear problems. It is shown that Schwartz distributions embedded into our new spaces of generalized functions, with…

Functional Analysis · Mathematics 2014-07-25 Stevan Pilipovic , Dimitris Scarpalezos , Jasson Vindas

In this letter, we give a characterization for a generic construction of bent functions. This characterization enables us to obtain another efficient construction of bent functions and to give a positive answer on a problem of bent…

Information Theory · Computer Science 2024-03-12 Yanjun Li , Jinjie Gao , Haibin Kan , Jie Peng , Lijing Zheng , Changhui Chen

In this work we consider a family of function classes constructed by means of the Gauss hypergeometric function $_2F_1(1,1;2;z) =-\frac{\log(1-z)}{z}$. We demonstrate that this family, in fact, constitutes classes of analytic functions…

Complex Variables · Mathematics 2025-12-29 Fiana Jacobzon

In this note we explore the relationship between the operation of convolution of functions and the Eulerian integrals. This approach allow us to obtain some expressions for the convolution of a certain class of functions in terms of the…

History and Overview · Mathematics 2024-02-27 Francisco Mota

In this paper we deal with the generalized Gamma processes and their compositions. For the compositions of two or more than two generalized Gamma processes we give, when possible, the explicit law whereas, in the other cases the…

Probability · Mathematics 2009-12-27 Mirko D'Ovidio

We define Bernstein-Sato polynomials for meromorphic functions and study their basic properties. In particular, we prove a Kashiwara-Malgrange type theorem on their geometric monodromies, which would be useful also in relation with the…

Complex Variables · Mathematics 2023-05-08 Kiyoshi Takeuchi

We use the theory of Bernstein functions to analyze power law tail behavior with log-periodic perturbations which corresponds to self-similarity of the Bernstein functions. Such tail behavior appears in the context of semistable L\'evy…

Probability · Mathematics 2023-12-22 Peter Kern , Svenja Lage

We study the properties of different type of transforms by means of operational methods and discuss the relevant interplay with many families of special functions. We consider in particular the binomial transform and its generalizations. A…

Mathematical Physics · Physics 2010-10-11 G. Dattoli , E. Sabia

We study a general class of weighted shifts whose weights $\alpha$ are given by $\alpha_n = \sqrt{\frac{p^n + N}{p^n + D}}$, where $p > 1$ and $N$ and $D$ are parameters so that $(N,D) \in (-1, 1)\times (-1, 1)$. Some few examples of these…

Functional Analysis · Mathematics 2026-05-12 Chafiq Benhida , Raul E. Curto , George R. Exner

We prove that the functions Phi(x)=[Gamma(x+1)]^{1/x}(1+1/x)^x/x and log Phi(x) are Stieltjes transforms.

Classical Analysis and ODEs · Mathematics 2007-05-23 Christian Berg

The Hermite-Gauss basis functions have been extensively employed in classical and quantum optics due to their convenient analytic properties. A class of multivariate Hermite-Gauss functions, the anisotropic Hermite-Gauss functions, arise by…

Mathematical Physics · Physics 2021-07-29 Shlomi Steinberg , Ömer Eğecioğlu , Ling-Qi Yan

In this paper, a new construction of quaternary bent functions from quaternary quadratic forms over Galois rings of characteristic 4 is proposed. Based on this construction, several new classes of quaternary bent functions are obtained, and…

Discrete Mathematics · Computer Science 2013-09-03 Baofeng Wu , Dongdai Lin

By replacing the Euler gamma function by the Barnes double gamma function in the definition of the Meijer $G$-function, we introduce a new family of special functions, which we call $K$-functions. This is a very general class of functions,…

Classical Analysis and ODEs · Mathematics 2024-03-12 Dmitrii Karp , Alexey Kuznetsov

We investigate the asymptotic behavior of parametric Bayes estimators under a broad class of loss functions that extend beyond the classical translation-invariant setting. To this end, we develop a unified theoretical framework for loss…

Statistics Theory · Mathematics 2026-03-16 Robin Requadt , Housen Li , Axel Munk

The paper presents new and known results on estimates of important linear and nonlinear approximation characteristics of generalized Wiener classes of functions of several variables in different metrics.

Classical Analysis and ODEs · Mathematics 2026-01-06 Andrii Shidlich

We prove some basic properties of quasinearly subharmonic functions and quasinearly subharmonic functions in the narrow sense.

Complex Variables · Mathematics 2016-08-17 Mansour Kalantar

In this paper our aim is to find the radii of $\gamma$-Spirallike of order $\alpha$ and convex $\gamma$-Spirallike of order $\alpha$ for three different kinds of normalizations of the function…

Complex Variables · Mathematics 2022-11-24 Sercan Kazımoğlu , Kamaljeet Gangania

An inequality concerning ratios of gamma functions is proved. This answers a question of Guo and Qi (2003).

Classical Analysis and ODEs · Mathematics 2009-09-22 Yaming Yu

We give an introduction to a theory of b-functions, i.e. Bernstein-Sato polynomials. After reviewing some facts from D-modules, we introduce b-functions including the one for arbitrary ideals of the structure sheaf. We explain the relation…

Algebraic Geometry · Mathematics 2007-05-23 Morihiko Saito

The general properties of two-dimensional generalized Bessel functions are discussed. Various asymptotic approximations are derived and applied to analyze the basic structure of the two-dimensional Bessel functions as well as their nodal…

Quantum Physics · Physics 2008-08-12 H. J. Korsch , A. Klumpp , D. Witthaut