Khan, K.N. and Lamb, W. and McBride, A.C. (2009) Fractional transformations of generalised functions. Integral Transforms and Special Functions, 20 (6). pp. 471490. ISSN 10652469

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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 

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 
Depositing user:  Mrs Carolynne Westwood 
Date Deposited:  10 Nov 2009 16:34 
Last modified:  24 Jul 2015 10:34 
URI:  http://strathprints.strath.ac.uk/id/eprint/13377 
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