1.

Record Nr.

UNINA9910450708903321

Autore

Rofe-Beketov Fedor S

Titolo

Spectral analysis of differential operators [[electronic resource] ] : interplay between spectral and oscillatory properties / / Fedor S. Rofe-Beketov, Aleksandr M. Kholkin ; translated by Ognjen Milatovic ; with foreword by Vladimir A. Marchenko

Pubbl/distr/stampa

Hackensack, NJ, : World Scientific, c2005

ISBN

1-281-90582-8

9786611905828

981-270-345-4

Descrizione fisica

1 online resource (463 p.)

Collana

World Scientific monograph series in mathematics ; ; v. 7

Altri autori (Persone)

KholʹkinAleksandr M

MilatovicOgnjen

Disciplina

515/.7222

Soggetti

Spectral theory (Mathematics)

Differential operators

Selfadjoint operators

Hilbert space

Operator theory

Electronic books.

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references (p. 359-429) and index.

Nota di contenuto

Foreword; Contents; Preface; Acknowledgments; Introduction; 1. Relation Between Spectral and Oscillatory Properties for the Matrix Sturm-Liouville Problem; 2. Fundamental System of Solutions for an Operator Differential Equation with a Singular Boundary Condition; 3. Dependence of the Spectrum of Operator Boundary Problems on Variations of a Finite or Semi-Infinite Interval; 4. Relation Between Spectral and Oscillatory Properties for Operator Differential Equations of Arbitrary Order

5. Self-Adjoint Extensions of Systems of Differential Equations of Arbitrary Order on an Infinite Interval in the Absolutely Indefinite Case6. Discrete Levels in Spectral Gaps of Perturbed Schrodinger and Hill Operators; Appendix A Self-Adjoint Extensions of Differential Opera- tors on a Finite Interval in Spaces of Vector-Functions;



Bibliography; List of Symbols; Index

Sommario/riassunto

This is the first monograph devoted to the Sturm oscillatory theory for infinite systems of differential equations and its relations with the spectral theory. It aims to study a theory of self-adjoint problems for such systems, based on an elegant method of binary relations. Another topic investigated in the book is the behavior of discrete eigenvalues which appear in spectral gaps of the Hill operator and almost periodic Schrödinger operators due to local perturbations of the potential (e.g., modeling impurities in crystals). The book is based on results that have not been presented in other