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

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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.

Item type: | Article |
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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 |

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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 |

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