Overview
- This book is open access, which means that you have free and unlimited access
- First time treatment of inverse problems in detail
- Numerous examples from physics included
- Open questions at the end of several chapters
Part of the book series: Operator Theory: Advances and Applications (OT, volume 293)
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Table of contents (24 chapters)
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Front Matter
Keywords
About this book
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.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Spectral Geometry of Graphs
Authors: Pavel Kurasov
Series Title: Operator Theory: Advances and Applications
DOI: https://doi.org/10.1007/978-3-662-67872-5
Publisher: Birkhäuser Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s) 2024
Hardcover ISBN: 978-3-662-67870-1Published: 09 November 2023
eBook ISBN: 978-3-662-67872-5Published: 07 November 2023
Series ISSN: 0255-0156
Series E-ISSN: 2296-4878
Edition Number: 1
Number of Pages: XVI, 639
Number of Illustrations: 63 b/w illustrations, 64 illustrations in colour
Topics: Quantum Computing, Partial Differential Equations, Systems Theory, Control, Calculus of Variations and Optimal Control; Optimization