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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    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.

    Author(s):Khan, Khaula Naeem, Lamb, Wilson ORCID logoORCID: https://orcid.org/0000-0001-8084-6054 and McBride, Adam C.
    Item type:Article
    ID code:13377
    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:07 Nov 2019 09:02
    URI:https://strathprints.strath.ac.uk/id/eprint/13377
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