Heisenberg–Weyl Groups and Generalized Hermite Functions

Monogenic Generalized Laguerre and Hermite Polynomials and Related Functions

Abstract. In recent years classical polynomials of a real or complex variable and their generalizations to the case of several real or complex variables have been in a focus of increasing attention leading to new and interesting problems. In this paper we construct higher dimensional analogues to generalized Laguerre and Hermite polynomials as well as some based functions in the framework of Cl...

Hermite-hadamard-type Inequalities for Generalized Convex Functions

The aim of the present paper is to extend the classical Hermite-Hadamard inequality to the case when the convexity notion is induced by a Chebyshev system.

Generalized Hermite-Padé approximation for Nikishin systems of three functions

Nikishin systems of three functions are considered. For such systems, the rate of convergence of simultaneous interpolating rational approximations with partially prescribed poles is studied. The solution is described in terms of the solution of a vector equilibrium problem in the presence of a vector external field.

Generalized Hermite Interpolation via Matrix-valued Conditionally Positive Definite Functions

In this paper, we consider a broad class of interpolation problems, for both scalarand vector-valued multivariate functions subject to linear side conditions, such as being divergence-free, where the data are generated via integration against compactly supported distributions. We show that, by using certain families of matrix-valued conditionally positive definite functions, such interpolation ...

Schwartz functions, Hermite functions, and the Hermite operator