Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-26T02:05:08.627Z Has data issue: false hasContentIssue false
  • English
  • Français

A distributional approach to Namias' fractional Fourier transforms

Published online by Cambridge University Press:  14 November 2011

Fiona H. Kerr
Fiona H. Kerr
Affiliation:
Department of Mathematics, University of Strathclyde, Glasgow Gl 1XH, Scotland, U.K.
Get access Rights & Permissions [Opens in a new window]

Synopsis

A fractionalisation of the Fourier transform was developed formally by Namias. By workingin ℐ, we found that this theory could be made mathematically rigorous. Here we extend our previous results to the space ℐ′ to consider fractional powers of the distributional Fourier transform. The paper concludes with an application to an ordinary differential equation which shows how a distributional approach can sometimes be more useful than a classical approach.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 108 , Issue 1-2 , 1988 , pp. 133 - 143
Copyright
Copyright © Royal Society of Edinburgh 1988

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Erdélyi, A.. From Delta Functions to Distributions. In Modern Mathematics for the Engineer (second series), 5–50 (New York: McGraw-Hill, 1961).Google Scholar
2Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.. Tables of IntegralTransforms, vol I (New York: McGraw-Hill, 1954).Google Scholar
3Love, E. R.. Changing the Order of Integration. J. Austral. Math. Soc. Ser. A 11 (1970), 421–432.Google Scholar
4McBride, A. C. and Kerr, F. H.. On Namias' Fractional Fourier Transforms. IMA J. Appl. Math. (to appear).Google Scholar
5Namias, V.. The Fractional Order Fourier Transform and its Application to Quantum Mechanics. J. Inst. Maths. Applies. 25(3) (1980), 241–265.Google Scholar