Composite Surfaces and Spectral Theory on Hilbert Spaces with Global Integral for Composition Operators

Abstract

Classical composition operators acting on Hardy spaces of holomorphic functions correspond to a special case. Are Shan main results provide characterizations of when the operators we introduce are bounded or compact. Dependence on the relations between the characterizations for the different operators are also studied .Novel continuous composite surfaces are presented which possess a high degree of multistability. Inspired by the illustrative behaviour of a multistable analog model, we show how two identical bitable composite shells with tailored asymmetric bistability may be connected to form a continuous quad stable surface. A spectral theory of linear operators on Hilbert spaces is developed under the assumptions that a linear operator on a Hilbert space is a perturbation of a self-adjoint operator, and the spectral measure of the self-adjoint operator has an analytic continuation near the real axis. The aim is to characterize boundedness and compactness of such operators in terms of global area integrals.