Extension Theory of Symmetric Operators and Boundary Value Problems / by Volodymyr Derkach, Mark Malamud.

Format:

Book

Author/Creator:

Derkach, Volodymyr., Author.

Malamud, Mark., Author.

Series:

Operator Theory: Advances and Applications, 2296-4878 ; 309

Language:

English

Subjects (All):

Operator theory.

Operator Theory.

Local Subjects:

Operator Theory.

Physical Description:

1 online resource (XII, 934 p. 1 illus.)

Edition:

2nd ed. 2025.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2025.

Summary:

This book presents the results obtained by the authors over the last four decades in the extension theory of symmetric operators in Hilbert spaces. First, some classic results are highlighted, influenced primarily by Krein, Vishik and Birman. Then, the method of boundary triples is discussed, demonstrating the universal character of the Weyl function which arises naturally both in problems of mathematical physics and classical interpolation problems. Readers of this book will gain an insight into the impressive construction of extension theory and its applications to problems in mathematical physics and analysis.

Contents:

- 1. Introduction

2. Unbounded Linear Operators

3. Extension Theory of Symmetric Operators

4. Semibounded Operators and Forms

5. Block Operator Matrices and Kreĭn’s Extension Theory of Non-Negative Operators

6. Herglotz–Nevanlinna Functions

7. Linear Relations

8. Boundary Triples, Proper Extensions and Weyl Functions

9. Boundary Triples and Extension Theory of Non-Negative Operators

10. Boundary Triples and Extension Theory of Operators with Gaps

11. Sturm–Liouville Operator

12. Extension Theory for Non-Densely Defined Symmetric Operator

13. Functional Models of Symmetric and Selfadjoint Operators

14. Characteristic Functions and Resolvent Matrices.

ISBN:

3-032-02967-8