Representation of fractional powers of infinitesimal generators of cosine operator functions (Q1056889)

By elementary means from the calculus of integral transforms we give a representation of fractional powers of the infinitesimal generator \(\Lambda\) of an equibounded \(C_ 0\)-cosine operator function C on a Banach space A. The result can be used in the theory of interpolation spaces concerning the characterization of the domains \(D((- \Lambda)^{\alpha})\), \(0<\alpha <r\), \(r\in N\), as intermediate spaces of A and \(D(\Lambda^ r)\).