Spectral Theory of Guided Waves represents a distillation of the authors' (and others) efforts over several years to rigorously discuss many of the properties of guided waves. The bulk of the book deals with the properties of eigenwaves of regular waveguiding systems and relates these to a variety of physical situations and applications to illustrate their generality. The book also includes considerable discussion of the basic properties of normal waves with quadratic operator pencils. Unique in its coverage of these subjects, the book will be of interest to engineers, applied mathematicians, and physicists with a working knowledge of functional analysis and spectral theory.
Table of Contents
Preface. Introduction. General linear waveguiding systems. Basic properties of normal waves of regular waveguides associated with quadratic operator pencils. Spectrum of normal waves of regular waveguides associated with quadratic operator pencils. Behaviour of eigenwaves of regular waveguides associated with quadratic operator pencils under variation of their frequency or wavenumber. Dispersion theory for regular waveguides associated with quadratic operator pencils. Further dispersion properties of regular waveguides associated with quadratic operator pencils. Regular inhomogeneous anisotropic elastic waveguides: an implementation of the abstract theory. Various particular regular waveguides. Appendices. A: Complex conjugation of elements and operators of an abstract Hilbert space. B: Some functional spaces. Korn inequalities for domains ^D*W and C^D[h. References. Index.
"The book represents an important contribution to the modern mathematical theory of waves. It is of great interest for both mathematicians and specialists in applications."