Integral transforms and extended Voigt functions

Fast Computation of Voigt Functions via Fourier Transforms

This work presents a method of computing Voigt functions and their derivatives, to high accuracy, on a uniform grid. It is based on an adaptation of Fourier-transform based convolution. The relative error of the result decreases as the fourth power of the computational effort. Because of its use of highly vectorizable operations for its core, it can be implemented very efficiently in scripting ...

Supports of Functions and Integral Transforms

In this paper we apply a method of spectral theory of linear operators [10] to establish relations between the support of a function f on R with properties of its image Tf under a linear operator T : R → R. The classical approach uses analytic continuation of the image Tf into some complex domain (theorems of Paley-Wiener type [4, 5, 6, 7]), and therefore, could not apply to functions whose ima...

Integral Transforms of Functions with Restricted Derivatives

Entire Functions and Integral Transforms by Louis De Branges

for all complex z. The space is introduced in [7], where it is characterized by three axioms. If E(a, z) and E(b> z) are entire functions which satisfy (1), then 3C(E(&)) will be contained isometrically in 3C(E(b)) if these functions satisfy the hypotheses of Theorem VII of [8]. Isometric inclusions of spaces of entire functions are a basic idea in [9] and [lO]. A fundamental property of these ...

Application of some integral transforms and multiple hypergeometric functions in modeling randomly weighted average of some random variables

This article has no abstract.