Pavel Kurasov: Spectral Geometry of Graphs

Cover: 9783662678701 | Spectral Geometry of Graphs | Pavel Kurasov | Buch | xvi | Englisch

Rückseite: 9783662678701 | Spectral Geometry of Graphs | Pavel Kurasov | Buch | xvi | Englisch

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Sprache: Englisch

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Beschreibung

Self-contained introduction to the theory of quantum graphs
First time treatment of inverse problems in detail
Numerous examples from physics included
Open questions at the end of several chapters

Über den Autor

Pavel Kurasov is a professor at Stockholm University. He graduated in mathematical physics with Boris Pavlov at Leningrad University and in mathematical analysis with Jan Boman at Stockholm University. He is the author of more than 100 research articles and of the book on singular interactions of differential operators together with Sergio Albeverio.

Zusammenfassung

Self-contained introduction to the theory of quantum graphs

First time treatment of inverse problems in detail

Numerous examples from physics included

Open questions at the end of several chapters

Inhaltsverzeichnis

- 1. Very Personal Introduction. - 2. How to Define Differential Operators on Metric Graphs. - 3. Vertex Conditions. - 4. Elementary Spectral Properties of Quantum Graphs. - 5. The Characteristic Equation. - 6. Standard Laplacians and Secular Polynomials. - 7. Reducibility of Secular Polynomials. - 8. The Trace Formula. - 9. Trace Formula and Inverse Problems. - 10. Arithmetic Structure of the Spectrum and Crystalline Measures. - 11. Quadratic Forms and Spectral Estimates. - 12. Spectral Gap and Dirichlet Ground State. - 13. Higher Eigenvalues and Topological Perturbations. - 14. Ambartsumian Type Theorems. - 15. Further Theorems Inspired by Ambartsumian. - 16. Magnetic Fluxes. - 17. M-Functions: Definitions and Examples. - 18. M-Functions: Properties and First Applications. - 19. Boundary Control: BC-Method. - 20. Inverse Problems for Trees. - 21. Boundary Control for Graphs with Cycles: Dismantling Graphs. - 22. Magnetic Boundary Control I: Graphs with Several Cycles. - 23. Magnetic Boundary Control II: Graphs on One Cycle and Dependent Subtrees. - 24. Discrete Graphs.

Details

Erscheinungsjahr:	2023
Fachbereich:	Theoretische Physik
Genre:	Mathematik , Medizin , Naturwissenschaften , Physik , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xvi 639 S. 63 s/w Illustr. 64 farbige Illustr. 639 p. 127 illus. 64 illus. in color.
ISBN-13:	9783662678701
ISBN-10:	3662678705
Sprache:	Englisch
Einband:	Gebunden
Autor:	Kurasov, Pavel
Hersteller:	Springer Birkhäuser Springer-Verlag GmbH
Verantwortliche Person für die EU:	Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße:	241 x 160 x 41 mm
Von/Mit:	Pavel Kurasov
Erscheinungsdatum:	09.11.2023
Gewicht:	1,139 kg