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 (https://doi.org/10.1080/10652460802646063)

Preview

Text. Filename: strathprints013377.pdf Accepted Author Manuscript Download (174kB)| 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.

ORCID iDs

Lamb, Wilson ORCID: https://orcid.org/0000-0001-8084-6054

• Share and Export
  

  EndNoteASCII CitationBibTeXDublin CoreMultiline CSVAtomEP3 XMLRDF+XMLSimple MetadataMPEG-21 DIDLRDF+N3RefWorksHTML CitationJSONRIS (EndNote Online, Zotero, Ref manager, etc)MODSMETSReferData Cite XMLRIOXX2 XMLRDF+N-TriplesOpenURL ContextObject in SpanOpenURL ContextObject
• Item metadata

  Item type:	Article
  ID code:	13377
  Dates:	Date Event 13 May 2009 Published
  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:	13 Dec 2024 22:17
  URI:	https://strathprints.strath.ac.uk/id/eprint/13377