Exponential type distributions and a generalized functional calculus for generators of $C_0$-groups

Abstract

The properties of a dual space to a space of entire functions of exponential type of many complex variables, that on the real subspace belongs to $L_p(\mathbb R^n)$ $(1\le p<\infty)$ are described. A functional calculus for generators of strongly continuous groups of bounded linear operators on an arbitrary Banach space in a Fourier-image of such dual space is constructed.