, Volume 47, Issue 1, pp 29-35

On generators of integratedC-semigroups andC-cosine functions

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Abstract

The following two theorems are proved: (1) the generator of an exponentially equicontinuousn-times integratedC-cosine function also generates an exponentially equicontinuous [(n+1)/2]-times integratedC-semigroup; (2) IfA and −A are generators of exponentially equicontinuousn-times integratedC-semigroups, thenA 2 generates an exponentially equicontinuousn-times integratedC-cosine function.

Communicated by Jerome A. Goldstein