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ON MAXIMAL REGULARITY AND SEMIVARIATION OF COSINE OPERATOR FUNCTIONS

Published online by Cambridge University Press:  01 June 1999

D.-K. CHYAN ,
S.-Y. SHAW  and
S. PISKAREV
D.-K. CHYAN
Affiliation:
Department of Mathematics, National Central University, Chung-Li, Taiwan 320 Current address: Hwa Hsia College of Technology and Commerce, Chung Ho, Taiwan
S.-Y. SHAW
Affiliation:
Department of Mathematics, National Central University, Chung-Li, Taiwan 320
S. PISKAREV
Affiliation:
Science Research Computer Center, Moscow State University, Vorobjevye Gory, Moscow 119899, Russia
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Abstract

It is proved that a cosine operator function C(·), with generator A, is locally of bounded semivariation if and only if u″(t) = Au(t)+f(t), t>0, u(0), u′(0)∈D(A), has a strong solution for every continuous function f, if and only if the function ∫t0∫t−s0C(τ) f(s)dτds, t>0, is twice continuously differentiable for every continuous function f, that is, C(·) has the maximal regularity property if and only if A is a bounded operator. Some other characterisations of bounded generators of cosine operator functions are also established in terms of their local semivariations.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 59 , Issue 3 , June 1999 , pp. 1023 - 1032
Copyright
The London Mathematical Society 1999

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