Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-25T05:50:34.534Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Range and Invertibility of a Class of Melon Multiplier Transforms III

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, LivingstoneTower, 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 continue to develop the theory of previous papers concerning transforms corresponding to Mellin multipliers which involve products and/or quotients of Γ-functions. We show that, by working with certain subspaces of Lp,μ consisting of smooth functions, we can simplify considerably the restrictions on the parameters which were necessary in the Lp,μ setting. As a result, operators in our class become homeomorphisms on these subspaces under conditions of great generality.

Keywords

42A4544A15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 6 , 01 December 1991 , pp. 1323 - 1338
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Erdélyi, A. et al., Higher transcendental functions, Vol. I. 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 ordinary differential operators, Proc. London Math. Soc. (3)45(1982), 519–546.Google Scholar
4. McBride, A.C., Fractional powers of a class of Mellin multiplier transforms II, Appl. Anal. 21(1986), 129–149.Google Scholar
5. McBride, A.C. and Spratt, W.J., On the range and invertibility of a class of Mellin multiplier transforms I, J. Math. Anal. Appl., 156(1991), 568–587.Google Scholar
6. McBride, A.C., On the range and invertibility of a class of Mellin multiplier transforms II, submitted.Google Scholar
7. McBride, A.C., A class of Mellin multipliers, Canad. Math. Bull., to appear.Google Scholar
8. 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
9. McBride, A.C., On integral transforms with G-function kernels, Proc. Royal Soc. Edinburgh, 93A( 1983), 265–297.Google Scholar
10. Spratt, W.J., A classical and distributional theory of Mellin multiplier transforms. Ph.D. thesis, University of Strathclyde, Glasgow, 1985.Google Scholar
11. Sprinkhuizen-Kuyper, I.G., A fractional integral operator corresponding to negative powers of a certain second order differential operator, J. Math. Anal. Appl. 72(1979), 674–702.Google Scholar
12. Tréves, F., Topological vector spaces, distributions and kernels. Academic Press, New York, 1967.Google Scholar
13. Zemanian, A.H., Generalized integral transformations. Interscience, New York, 1968.Google Scholar