Fractional transformations of generalised functions

Khan, Khaula Naeem and Lamb, Wilson and McBride, Adam C. (2009) Fractional transformations of generalised functions. Integral Transforms and Special Functions, 20 (6). pp. 471-490. ISSN 1065-2469

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Official URL: https://doi.org/10.1080/10652460802646063

Abstract

A distributional theory of fractional transformations is developed. A constructive approach, based on the eigenfunction expansion method pioneered by A. H. Zemanian, is used to produce an appropriate space of test functions and corresponding space of generalised functions. The fractional transformations that are defined are shown to form an equicontinuous group of operators on the space of test functions and a weak continuous group on the space of generalised functions. Integral representations for the fractional transformations are also obtained under certain conditions. The fractional Fourier transformation is considered as a particular case of our general theory.

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Khan, Khaula Naeem, Lamb, Wilson

and McBride, Adam C.;

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Item metadata

Item type:	Article
ID code:	13377
Dates:	Date Event 13 May 2009 Published
Keywords:	fractional integral transforms, semigroups of operators, generalised functions, mathematics, statistics, Mathematics, Statistics, Analysis, Applied Mathematics
Subjects:	Science > Mathematics Social Sciences > Statistics
Department:	Faculty of Science > Mathematics and Statistics > Mathematics Faculty of Science > Mathematics and Statistics
Depositing user:	Mrs Carolynne Westwood
Date deposited:	10 Nov 2009 16:34
Last modified:	25 Apr 2021 00:17
URI:	https://strathprints.strath.ac.uk/id/eprint/13377

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