On general cosine operator function in Banach space. (English) Zbl 1480.47065
Summary: In this paper we explain our motivation for introducing a new definition of cosine operator function in Banach space and then, along with an appropriate explanation, we introduce a new definition of cosine operator function and its infinitesimal
generator. We give relevant comparison and draw a parallel with an earlier
definition of these functions as solutions of D’Alembert equation.
MSC:
47D09 | Operator sine and cosine functions and higher-order Cauchy problems |
39B22 | Functional equations for real functions |
39B42 | Matrix and operator functional equations |