We introduce a generalized Crofoot transform between the model spaces corresponding to matrix-valued inner functions. As an application, we obtain results about truncated Toeplitz operators.

We write down the generalized Bessel function associated with the root system of type D by means of multivariate hypergeometric series. Our hint comes from the particular case of the Brownian motion in the Weyl chamber of type D.

The purpose of the present paper is to derive the necessary and sufficient condition for the generalized Bessel function (struve function) belonging to the classes Ωλ(g;α, β) and Υ ∗ λ(g;α, β).

We propose a new method for the numerical evaluation of the spherical Bessel transform. A formula is derived for the transform by using an integral representation of the spherical Bessel function and by changing the integration variable. The resultant algorithm consists of a set of the Fourier transforms and numerical integrations over a linearly spaced grid of variable k in Fourier space. Beca...

We review the Fourier-Laguerre transform, an alternative harmonic analysis on the three-dimensional ball to the usual Fourier-Bessel transform. The Fourier-Laguerre transform exhibits an exact quadrature rule and thus leads to a sampling theorem on the ball. We study the definition of convolution on the ball in this context, showing explicitly how translation on the radial line may be viewed as...

In this note we give a generalization of a result of Aronszajn and Smith [l] concerning sections of exceptional sets for the spaces of Bessel potentials on Rn of L2 functions and restrictions of functions in these spaces. For the sake of completeness we recall briefly the relevant definitions and theorems. We refer for details to [2]. Throughout this paper we will be concerned with functions de...

This paper introduces a new method for the development of closed-form spatial Green’s functions for electrostatic problems involving layered dielectrics. The new method utilizes a finite-difference approximation of the spectral domain form of the Green’s function to overcome the tedious numerical integration of the Fourier–Bessel inverse transform that is required to generate the Green’s functi...