Operators and Semigroups for Systems with Boundary Inputs

Abstract

We assume basic knowledge of functional analysis and Laplace transformation as can be found in standard books. In order to fix the notations, first we recall general and well known properties. Then we describe the specific instruments of functional analysis which we use in the study of systems with boundary inputs: Laplace transformation and Hardy spaces of vector valued functions; extension of an operator by transposition and extrapolation spaces; fractional powers of selfadjoint positive operators; Sobolev spaces; the Laplace equation with nonhomogeneous Dirichlet and Neumann boundary conditions; semigroup and cosine operators. Then we describe the way these tools can be used to model systems with boundary inputs.