Denseness, Bases and Frames in Banach Spaces and Applications

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
ν-convergence operators
Γ-hypercyclic set of linear operators
Analytic operators in Béla Szökefalvi-Nagy’s sense
Bases of the perturbed operator T(ε)
Frame of the perturbed operator T(ε)
Perturbation method for sound radiation by a vibrating plate in a light fluid
Applications to mathematical models
Reggeon field theory