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On Hankel transform and Hankel convolution of Beurling type distributions having upper bounded support

M. Belhadj, Jorge J. Betancor (2004)

Czechoslovak Mathematical Journal

In this paper we study Beurling type distributions in the Hankel setting. We consider the space ( w ) ' of Beurling type distributions on ( 0 , ) having upper bounded support. The Hankel transform and the Hankel convolution are studied on the space ( w ) ' . We also establish Paley Wiener type theorems for Hankel transformations of distributions in ( w ) ' .

On K-transform.

Nasim, C. (1981)

International Journal of Mathematics and Mathematical Sciences

On Some Generalizations of Classical Integral Transforms

Virchenko, Nina (2012)

Mathematica Balkanica New Series

MSC 2010: 44A15, 44A20, 33C60Using the generalized confluent hypergeometric function [6] some new integral transforms are introduced. They are generalizations of some classical integral transforms, such as the Laplace, Stieltjes, Widder-potential, Glasser etc. integral transforms. The basic properties of these generalized integral transforms and their inversion formulas are obtained. Some examples are also given.

On some singular integral operatorsclose to the Hilbert transform

T. Godoy, L. Saal, M. Urciuolo (1997)

Colloquium Mathematicae

Let m: ℝ → ℝ be a function of bounded variation. We prove the L p ( ) -boundedness, 1 < p < ∞, of the one-dimensional integral operator defined by T m f ( x ) = p . v . k ( x - y ) m ( x + y ) f ( y ) d y where k ( x ) = j 2 j φ j ( 2 j x ) for a family of functions φ j j satisfying conditions (1.1)-(1.3) given below.

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