Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-27T06:24:01.783Z Has data issue: false hasContentIssue false
  • English
  • Français

Fractional powers of a closed pair of operators

Published online by Cambridge University Press:  14 November 2011

Marié Grobbelaar-Van Dalsen
Marié Grobbelaar-Van Dalsen
Affiliation:
University of South Africa, P.O. Box 392, Pretoria, 0001 South Africa
Get access Rights & Permissions [Opens in a new window]

Synopsis

In this paper we introduce the concept of fractional powers of a pair of operators between two Banach spaces. The operators need not be closed, but form a closed pair. The properties of the fractional powers are studied. An application of the theory is briefly discussed.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 102 , Issue 1-2 , 1986 , pp. 149 - 158
Copyright
Copyright © Royal Society of Edinburgh 1986

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

1Kato, T.. Fractional Powers of Dissipative Operators. J. Math. Soc. Japan 13 (1961), 246–274.CrossRefGoogle Scholar
2Sauer, N.. Linear Evolution Equations in two Banach Spaces. Pretoria Univ. Dept Appl. Math. Res. Report UPTW 17 (1980).Google Scholar
3Sauer, N.. Linear Evolution Equations in two Banach Spaces. Proc. Roy. Soc. Edinburgh Sect. A 91 (1982), 287–303.CrossRefGoogle Scholar
4Sauer, N. and van der Merwe, A.. Eigenvalue Problems with the Spectral Parameter also in the Boundary Condition. Quaestiones Math. 5 (1982), 1–27.CrossRefGoogle Scholar
5Sobolevski, P. E.. On Equations of Parabolic Type in a Banach Space. Trudy Moscov. Mat. Obšč. 10 (1961), 297–350.Google Scholar
6van Dalsen, M.. Die Teorie van Nie-Stasionêre Evolusies geassosieer met Dinamies-Gekoppelde Randwaardeprobleme. (Doctoral Thesis: Pretoria University, 1978).Google Scholar
7Yosida, K.. Fractional Powers of Infinitesimal Generators and Analyticity of the Semigroup generated by them. Proc. Japan Acad. 36 (1960), 86–89.Google Scholar
8Yosida, K.. Functional Analysis (Berlin: Springer, 1980).Google Scholar