Strathprints Home | Open Access | Browse | Search | User area | Copyright | Help | Library Home | SUPrimo

Fractional transformations of generalised functions

Khan, K.N. and Lamb, W. and McBride, A.C. (2009) Fractional transformations of generalised functions. Integral Transforms and Special Functions, 20 (6). pp. 471-490. ISSN 1065-2469

[img]
Preview
PDF (strathprints013377.pdf)
Download (249Kb) | Preview

    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.

    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
    Faculty of Science > Mathematics and Statistics > Mathematics
    Related URLs:
      Depositing user: Mrs Carolynne Westwood
      Date Deposited: 10 Nov 2009 16:34
      Last modified: 04 Sep 2014 23:22
      URI: http://strathprints.strath.ac.uk/id/eprint/13377

      Actions (login required)

      View Item

      Fulltext Downloads: