Fractional transformations of generalised functions

Khaula Naeem Khan, Wilson Lamb, Adam C. McBride

Research output: Contribution to journalArticle

5 Citations (Scopus)

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.
LanguageEnglish
Pages471-490
Number of pages20
JournalIntegral Transforms and Special Functions
Volume20
Issue number6
DOIs
Publication statusPublished - 13 May 2009

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Generalized Functions
Fractional
Test function
Eigenfunction Expansion
Fourier Transformation
Eigenvalues and eigenfunctions
Integral Representation
Mathematical operators
Operator

Keywords

  • fractional integral transforms
  • semigroups of operators
  • generalised functions
  • mathematics
  • statistics

Cite this

Khan, Khaula Naeem ; Lamb, Wilson ; McBride, Adam C. / Fractional transformations of generalised functions. In: Integral Transforms and Special Functions. 2009 ; Vol. 20, No. 6. pp. 471-490.
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Fractional transformations of generalised functions. / Khan, Khaula Naeem; Lamb, Wilson; McBride, Adam C.

In: Integral Transforms and Special Functions, Vol. 20, No. 6, 13.05.2009, p. 471-490.

Research output: Contribution to journalArticle

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KW - semigroups of operators

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KW - mathematics

KW - statistics

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