Hostname: page-component-669899f699-vbsjw Total loading time: 0 Render date: 2025-04-27T00:10:33.294Z Has data issue: false hasContentIssue false
  • English
  • Français

Fractional powers of operators and Riesz fractional integrals

Published online by Cambridge University Press:  14 November 2011

S. E. Schiavone
S. E. Schiavone
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
Get access Rights & Permissions [Opens in a new window]

Synopsis

In this paper, a theory of fractional powers of operators due to Balakrishnan, which is valid for certain operators on Banach spaces, is extended to Fréchet spaces. The resultingtheory is shown to be more general than that developed in an earlier approach by Lamb, and is applied to obtain mapping properties of certain Riesz fractional integral operators on spaces of test functions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 112 , Issue 3-4 , 1989 , pp. 237 - 247
Copyright
Copyright © Royal Society of Edinburgh 1989

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.)

Article purchase

Temporarily unavailable

References

1Balakrishnan, A. V.. Fractional powers of closed operators and the semigroups generated by them. Pacific J. Math. 10 (1960), 419–437.CrossRefGoogle Scholar
2Lamb, W.. Fractional Powers of Operators on Frechet Spaces with Applications (Ph.D. Thesis, Strathclyde University, 1980).Google Scholar
3Lamb, W.. Fractional powers of operators denned on a Frechet space. Proc. Edinburgh Math. Soc. (2) 27 (1984), 165–180.Google Scholar
4Lamb, W.. A distributional theory of fractional calculus. Proc. Roy. Soc. Edinburgh Sect. A 99 (1985), 347–357.Google Scholar
5Ryshik, I. M. and Gradstein, I. S.. Tafeln Tables (Berlin: Veb Deutscher Verlag der Wissenschaften, 1957).Google Scholar
6Schiavone, S. E.. Distributional Theories for Multidimensional Fractional Integrals and Derivatives (Ph.D. Thesis, Strathclyde University, 1988).Google Scholar
7Schiavone, S. E. and Lamb, W.. A fractional power approach to fractional calculus. J. Math. Anal. Appl. (to appear).Google Scholar
8Yosida, K.. Functional analysis, 5th edn (Berlin: Springer, 1978).Google Scholar
9Zemanian, A. H.. Generalized Integral Transformations (New York: Interscience, 1968).Google Scholar