Integral transforms of functions with restricted derivatives

Integral Transforms of Functions with Restricted Derivatives

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...

Using Integral Transforms to Estimate Higher Order Derivatives

When doing error analysis for numerical quadrature, achieving good uniform bounds on higher order derivatives of the integrand is paramount. As undergraduates become increasingly adept with programmable calculators, numerical integration schemes such as Simpson’s Rule and the Trapezoidal Rule take on a new relevance. Although it may be a rare calculus class that dwells overmuch on error bounds ...

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

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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 ...