Spectral Geometry of Graphs: 293 (Operator Theory: Advances and Applications, 293) - Tapa dura

Kurasov, Pavel

 
9783662678701: Spectral Geometry of Graphs: 293 (Operator Theory: Advances and Applications, 293)
Tapa dura
ISBN 10: 3662678705 ISBN 13: 9783662678701
Editorial: Birkhäuser, 2023

Sinopsis

This open access book gives a systematic introduction into the spectral theory of differential operators on metric graphs. Main focus is on the fundamental relations between the spectrum and the geometry of the underlying graph.


The book has two central themes: the trace formula and inverse problems.

The trace formula is relating the spectrum to the set of periodic orbits and is comparable to the celebrated Selberg and Chazarain-Duistermaat-Guillemin-Melrose trace formulas. Unexpectedly this formula allows one to construct non-trivial crystalline measures and Fourier quasicrystals solving one of the long-standing problems in Fourier analysis. The remarkable story of this mathematical odyssey is presented in the first part of the book.

To solve the inverse problem for Schrödinger operators on metric graphs the magnetic boundary control method is introduced. Spectral data depending on the magnetic flux allow one to solve the inverse problem in full generality, this means to reconstruct not only the potential on a given graph, but also the underlying graph itself and the vertex conditions.

The book provides an excellent example of recent studies where the interplay between different fields like operator theory, algebraic geometry and number theory, leads to unexpected and sound mathematical results. The book is thought as a graduate course book where every chapter is suitable for a separate lecture and includes problems for home studies. Numerous illuminating examples make it easier to understand new concepts and develop the necessary intuition for further studies.

"Sinopsis" puede pertenecer a otra edición de este libro.

Acerca del 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.

De la contraportada

This open access book gives a systematic introduction into the spectral theory of differential operators on metric graphs. Main focus is on the fundamental relations between the spectrum and the geometry of the underlying graph.


The book has two central themes: the trace formula and inverse problems.

The trace formula is relating the spectrum to the set of periodic orbits and is comparable to the celebrated Selberg and Chazarain-Duistermaat-Guillemin-Melrose trace formulas. Unexpectedly this formula allows one to construct non-trivial crystalline measures and Fourier quasicrystals solving one of the long-standing problems in Fourier analysis. The remarkable story of this mathematical odyssey is presented in the first part of the book.

To solve the inverse problem for Schrödinger operators on metric graphs the magnetic boundary control method is introduced. Spectral data depending on the magnetic flux allow one to solve the inverse problem in full generality, this means to reconstruct not only the potential on a given graph, but also the underlying graph itself and the vertex conditions.

The book provides an excellent example of recent studies where the interplay between different fields like operator theory, algebraic geometry and number theory, leads to unexpected and sound mathematical results. The book is thought as a graduate course book where every chapter is suitable for a separate lecture and includes problems for home studies. Numerous illuminating examples make it easier to understand new concepts and develop the necessary intuition for further studies.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Birkhäuser
Año de publicación
2023
Idioma
Inglés
ISBN 10 
3662678705
ISBN 13 
9783662678701
Encuadernación
Tapa dura
Número de edición
1
Número de páginas
656
Contacto del fabricante
no disponible
Persona responsable
no disponible