Hostname: page-component-788cddb947-55tpx Total loading time: 0 Render date: 2024-10-14T21:05:16.479Z Has data issue: false hasContentIssue false
  • English
  • Français

A Class of Mellin Multipliers

Published online by Cambridge University Press:  20 November 2018

A. C. McBride  and
W. J. Spratt
A. C. McBride
Affiliation:
Department of Mathematics University of Strathclyde, Livingstone Tower 26 Richmond Street Glasgow Gl 1XH Scotland
W. J. Spratt
Affiliation:
12 Hickory Close Lytchett Minster Poole, Dorset England
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We examine a class of functions which can serve as Mellin multipliers in the setting of the spaces Fp,μ which we have used extensively in other papers. The conditions to be satisfied by such a multiplier h do not involve h′ explicitly. This means that multipliers involving T-functions can be handled by means of the asymptotics of Γ(z) alone, without the need to study ψ = Γ′/Γ, thereby saving effort in the case of complicated multipliers.

Keywords

42A45.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 2 , 01 June 1992 , pp. 252 - 260
Copyright
Copyright © Canadian Mathematical Society 1992 

References

1. Erdélyi, A. et al., Higher Transcendental Functions, 1, McGraw-Hill, New York, (1953).Google Scholar
2. McBride, A. C., Fractional Calculus and Integral Transforms of Generalised Functions, Pitman, London, (1979).Google Scholar
3. McBride, A. C., Fractional powers of a class of Mellin multiplier transforms II, Appl. Anal., 21(1986), 129–149.Google Scholar
4. McBride, A. C. and Spratt, W. J., On the range and invertibility of a class of Mellin multiplier transforms I, J. Math. Anal. Appl., to appear.Google Scholar
5. McBride, A. C. and Spratt, W. J., On the range and invertibility of a class of Mellin multiplier transforms II, submitted.Google Scholar
6. McBride, A. C. and Spratt, W. J., On the range and invertibility of a class of Mellin multiplier transforms III, submitted.Google Scholar
7. Rooney, P. G., A technique for studying the boundedness and extendability of certain types of operators, Canad. J. Math. 25(1973), 1090–1102.Google Scholar
8. Spratt, W. J., A Classical and Distributional Theory of Mellin Multiplier Transforms, Ph. D. Thesis, University of Strathclyde, Glasgow, (1985).Google Scholar
9. Stein, E. M., Singular Integrals and the Differentiability Properties of Functions, University Press, Princeton, (1970).Google Scholar