Entire functions and integral transforms

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 ...

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...

On the Integral Representations of Generalized Relative Type and Generalized Relative Weak Type of Entire Functions

In this paper we wish to establish the integral representations of generalized relative type and generalized relative weak type as introduced by Datta et al [9]. We also investigate their equivalence relation under some certain conditions.

Integral Transforms of Functions with Restricted Derivatives

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

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