Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T00:42:14.743Z Has data issue: false hasContentIssue false

Fractional powers of operators defined on a Fréchet space

Published online by Cambridge University Press:  20 January 2009

W. Lamb
Affiliation:
Department of MathematicsUniversity of StrathclydeGlasgow
Rights & Permissions [Opens in a new window]

Extract

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.

The problem of finding a suitable representation for a fractional power of an operator defined in a Banach space X has, in recent years, attracted much attention. In particular, Balakrishnan [1], Hovel and Westphal [3] and Komatsu [4] have examined the problem of defining the fractionalpower (–A)α for closed densely-defined operators A such that

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1984

References

REFERENCES

1.Balakrishnan, A. V., Fractional powers of closed operators and semigroups generated by them, Pacific J. Math. 10 (1960), 419437.CrossRefGoogle Scholar
2.Erdelyi, A., et al. , Tables of integral transforms (vol. 2) (McGraw-Hill, New York, 1954).Google Scholar
3.Hovel, H. W. and Westphal, U., Fractional powers of closed operators, Studia Math. 42 (1972), 177194.CrossRefGoogle Scholar
4.Komatsu, H., Fractional powers of operators, Pacific J. Math. 19 (1966), 285346.CrossRefGoogle Scholar
5.Lamb, W., Fractional powers of operators on Frechet spaces with applications (Strathclyde Univ. Ph.D. Thesis, 1980).Google Scholar
6.Mcbride, A. C., A theory of fractional integration for generalised functions (Edinburgh Univ. Ph.D. Thesis, 1971).Google Scholar
7.Mcbride, A. C., Fractional calculus and integral transforms of generalized functions (Research Notes in Mathematics 31, Pitman, London 1979).Google Scholar
8.Okikiolu, G. O., Aspects of the theory of bounded integral operators in Lp-spaces (Academic Press, London, 1971).Google Scholar
9.Rudin, W., Functional analysis (Tata McGraw-Hill, New Delhi, 1974).Google Scholar
10.Watanabe, J., On some properties of fractional powers of linear operators, Proc. Japan Acad. 37 (1961), 273275.Google Scholar
11.Yosida, K., Functional analysis (3rd. ed.) (Springer, Berlin, 1971).CrossRefGoogle Scholar
12.Zemanian, A. H., Generalized integral transformations (Interscience, New York, 1968).Google Scholar