Cosine families of operators in a class of Fréchet spaces

Abstract

M. sova [10] proved that the infinitesimal generator of all uniformly continuous cosine family, of operators in Banach space, is a bounded operator. We show by counter-example that the result mentioned above is not true in general on Fréchet spaces, and we prove that the infinitesimal generator of an uniformly continuous cosine family of operators in a class of Fréchet spaces (quojection) is necessarily continuous.

Some results regarding observability and initial state reconstruction for time-fractional systems

“…For more details about strongly continuous cosine and sine families, we refer the reader to [38,39].…”