This book is devoted to recent developments concerning linear operators, covering topics such as the Cauchy problem, Riesz basis, frames, spectral theory and applications to the Gribov operator in Bargmann space.

Also, integral and integro-differential equations as well as applications to problems in mathematical physics and mechanics are discussed.

Contents

Introduction

Linear operators

Basic notations and results

Bases

Semi-groups

Discrete operator and denseness of the generalized eigenvectors

Frames in Hilbert spaces

Summability of series

?-convergence operators

G-hypercyclic set of linear operators

Analytic operators in Béla Szökefalvi-Nagy’s sense

Bases of the perturbed operator T(e)

Frame of the perturbed operator T(e)

Perturbation method for sound radiation by a vibrating plate in a light fluid

Applications to mathematical models

Reggeon field theory