Interpolation of cosine operator functions

Abstract

S u m m a r y . -Using basic techniques ]rom the theory of interpolation spaces equivalence theorems are established ]or the intermediate spaces between a given Banach space A and the domain D(A r) o] the r-th power o] the in]initesimal generator A o] a strongly conti~nwus cosine operator ]unction C. The results are applied to the study o] second order evolution equations including regularity, order reduetio;~ and approximation by ]inite di]]erence methods.1 . -I n t r o d u c t i o n .

Representation of complex powers of C-sectorial operators

“…The first of these two equalities has been proved by R.H.W. Hoppe in [16]. Further on, by taking γ = 1/2 in the second of these equalities, we get an old result of H.O.…”

“…c 2014 Diogenes Co., Sofia pp. 827-854 , DOI: 10.2478/s13540-014-0200- 6 Hoppe [15]- [16], established for strongly continuous cosine operator functions. We shall represent in Example 2.1 fractional powers of (almost) C-sectorial operators using the recent approach of J.E.…”

A note on interpolation of semigroups

“…We have already recalled the fundamental facts on integrated cosine functions. In order to obtain interpolation results, we need here an analogue of Proposition 2.3 (see Hoppe [15,Theorem 2.7]). Let Ca:= l0°°r2a-x(cost-l)dt.…”

“…Let Ca:= l0°°r2a-x(cost-l)dt. Taylor's formula for Co-semigroups (formula (2.5)) has an equivalent for operator cosine functions (see Hoppe [15]):…”