On Wallen-type formulae for integrated semigroups and sine functions

Abstract

Abstract. We prove Wallen-type formulae for integrated semigroups and sine functions with values in a unital Banach algebra with unit u. As the main application, we show that p(t) = tu, t ≥ 0 is an isolated integrated semigroup and sine function.Mathematics Subject Classification. 47D62, 47D09.