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In this paper we refer to the reconstruction formulas given in L.-E. Andersson's On the determination of a function from spherical averages, which are often used in applications such as SAR and SONAR. We demonstrate that the first one of…
We give a generalization of the random matrix ensembles, including all lassical ensembles. Then we derive the joint density function of the generalized ensemble by one simple formula, which give a direct and unified way to compute the…
Foundational material on complex Lie supergroups and their radial operators is presented. In particular, Berezin's recursion formula for describing the radial parts of fundamental operators in general linear and ortho-symplectic cases is…
We study the algebraic and geometric properties of the integral closure of different rings of functions on a real algebraic variety : the regular functions and the continuous rational functions.
We investigate the space $X$ of unitary hermitian matrices over $\frp$-adic fields through spherical functions. First we consider Cartan decomposition of $X$, and give precise representatives for fields with odd residual characteristic,…
Family of replica matrices, related to general ultrametric spaces, is introduced. These matrices generalize the known Parisi matrices. Some functionals of replica approach are computed.
A new representation for a regular solution of the radial Dirac system of a special form is obtained. The solution is represented as a Neumann series of Bessel functions uniformly convergent with respect to the spectral parameter. For the…
In this paper, we introduce new classes of functions that extend the known classes of functions of complex variable, such as entire functions, meromorphic functions, rational functions and polynomial functions and take values in the set of…
We deal with decay and boundedness properties of radial functions belonging to Besov and Lizorkin-Triebel spaces. In detail we investigate the surprising interplay of regularity and decay. Our tools are atomic decompositions in combination…
Sufficient conditions are determined on the parameters such that the generalized and normalized Bessel function of the first kind and other related functions belong to subclasses of starlike and convex functions defined in the unit disk…
It is established that general s-convex functions are a new class of generalized convex functions. In a similar vein, a new class of general s-convex sets is introduced, which are generalizations of s-convex sets. Additionally, certain…
We introduce and study new modules and spaces of generalized functions that are related to the classical Besov spaces. Various Schwartz distribution spaces are naturally embedded into our new generalized function spaces. We obtain precise…
In the field of radial basis functions mathematicians have been endeavouring to find infinitely differentiable and compactly supported radial functions. This kind of functions is extremely important. One of the reasons is that its error…
We report on a new class of exact solutions of the scalar Helmholtz equation obtained by carefully engineering the form of the angular spectrum of a Bessel beam. We consider in particular the case in which the angular spectrum of such…
Complex functions have multiple uses in various fields of study, so analyze their characteristics it is of extensive interest to other sciences. This work begins with a particular class of rational functions of a complex variable; over this…
In this paper we consider smoothness and decay properties of radial functions belonging to smoothness spaces related to Morrey spaces (Sobolev-Morrey spaces, Besov-type spaces and Besov-Morrey spaces). Within this framework we prove…
Matrix elements and spherical functions of irreducible representations of the de Sitter group are studied on the various homogeneous spaces of this group.
Let $ \mathcal{S}(p) $ be the class of all meromorphic univalent functions defined in the unit disc $ \mathbb{D} $ of the complex plane with a simple pole at $ z=p $ and normalized by the conditions $ f(0)=0 $ and $ f^{\prime}(0)=1 $. In…
Fractional vector calculus is discussed in the spherical coordinate framework. A variation of the Legendre equation and fractional Bessel equation are solved by series expansion and numerically. Finally, we generalize the hypergeometric…
In this work we develop an algebraic theory of linear recurrence equations and systems with constant coefficients and reflection. We obtain explicit solutions and the Green's functions associated to different problems under general linear…