The probabilistic representation formulae for cosine operator functions. (English) Zbl 0806.47038
Summary: We obtain general representation formulae for strongly continuous cosine operator functions via probabilistic approach, which include Webb’s and Shaw’s formulae and some new ones as special cases. We also give the quantitative estimations for the general formulae.
MSC:
47D09 | Operator sine and cosine functions and higher-order Cauchy problems |