Related papers: A unified representation-theoretic approach to spe…
We develop a representation theory approach to the study of generalized hypergeometric functions of Gelfand, Kapranov and Zelevisnky (GKZ). We show that the GKZ hypergeometric functions may be identified with matrix elements of…
We find a recursive expression for the Bessel function of S. I. Gelfand for irreducible generic representations of $\operatorname{GL}_n\left(\mathbb{F}_q\right)$. We show that special values of the Bessel function can be realized as the…
Most of the special functions of mathematical physics are connected with the representation of Lie groups. The action of elements $D$ of the associated Lie algebras as linear differential operators gives relations among the functions in a…
By introducing a kind of special functions namely exponent-like function, cosine-like function and sine-like function, we obtain explicitly the basic structures of solutions of initial value problem at the original point for this kind of…
Integrally convex functions constitute a fundamental function class in discrete convex analysis, including M-convex functions, L-convex functions, and many others. This paper aims at a rather comprehensive survey of recent results on…
An overview of the basic results on Macdonald(-Koornwinder) polynomials and double affine Hecke algebras is given. We develop the theory in such a way that it naturally encompasses all known cases. Among the basic properties of the…
The necessary and sufficient conditions for existence of a generalized representer theorem are presented for learning Hilbert space-valued functions. Representer theorems involving explicit basis functions and Reproducing Kernels are a…
This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…
Ultrafunctions are a particular class of functions defined on a hyperreal field $\mathbb{R}^{\ast}\supset\mathbb{R}$. They have been introduced and studied in some previous works. In this paper we introduce a particular space of…
Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…
There has recently been interest in relating properties of matrices drawn at random from the classical compact groups to statistical characteristics of number-theoretical L-functions. One example is the relationship conjectured to hold…
Let G be the group of points of a quasi-split reductive algebraic group over a local field F. It follows from the local Langlands conjectures that to every non-trivial additive character of F and every representation of the Langlands dual…
In previous work the framework for a hypercomplex function theory in superspace was established and amply investigated. In this paper a Cauchy integral formula is obtained in this new framework by exploiting techniques from orthogonal…
Ultrafunctions are a particular class of functions defined on a Non Archimedean field R^{*}\supset R. They have been introduced and studied in some previous works ([1],[2],[3]). In this paper we introduce a modified notion of ultrafunction…
We show that the method of separation of variables gives a natural generalisation of integral relations for classical special functions of one variable. The approach is illustrated by giving a new proof of the ``quadratic'' integral…
UNIFORM algebras have been extensively investigated because of their importance in the theory of uniform approximation and as examples of complex Banach algebras. An interesting question is whether analogous algebras exist when a complete…
Represented spaces form the general setting for the study of computability derived from Turing machines. As such, they are the basic entities for endeavors such as computable analysis or computable measure theory. The theory of represented…
Generating functions and functional equations of Dickson polynomials of the first and second kind are derived and continued analytically. These formulae are expressed in terms of the incomplete gamma function over complex variables of the…
Generalized matrix-fractional (GMF) functions are a class of matrix support functions introduced by Burke and Hoheisel as a tool for unifying a range of seemingly divergent matrix optimization problems associated with inverse problems,…
We survey the development and status quo of a subject best described as "generic representation theory of finite dimensional algebras", which started taking shape in the early 1980s. Let $\Lambda$ be a finite dimensional algebra over an…