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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.
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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.
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Spectral Geometry of Graphs
Publicado por
Springer Berlin Heidelberg Okt 2023, 2023
ISBN 10: 3662678705
ISBN 13: 9783662678701
Nuevo
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Librería: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Alemania
Calificación del vendedor: 5 de 5 estrellas
Buch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 656 pp. Englisch. Nº de ref. del artículo: 9783662678701
Cantidad disponible: 2 disponibles
Imagen del vendedor
Spectral Geometry of Graphs
Publicado por
Springer Berlin Heidelberg, 2023
ISBN 10: 3662678705
ISBN 13: 9783662678701
Nuevo
Tapa dura
Librería: AHA-BUCH GmbH, Einbeck, Alemania
Calificación del vendedor: 5 de 5 estrellas
Buch. Condición: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Nº de ref. del artículo: 9783662678701
Cantidad disponible: 1 disponibles
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Spectral Geometry of Graphs (Operator Theory: Advances and Applications, 293)
Librería: Ria Christie Collections, Uxbridge, Reino Unido
Calificación del vendedor: 5 de 5 estrellas
Condición: New. In. Nº de ref. del artículo: ria9783662678701_new
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Spectral Geometry of Graphs
Publicado por
Springer Berlin Heidelberg, 2023
ISBN 10: 3662678705
ISBN 13: 9783662678701
Nuevo
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Librería: moluna, Greven, Alemania
Calificación del vendedor: 5 de 5 estrellas
Condición: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This book is open access, which means that you have free and unlimited access.First time treatment of inverse problems in detailNumerous examples from physics includedOpen questions at the end of several chaptersPavel Kura. Nº de ref. del artículo: 913670709
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Spectral Geometry of Graphs (Operator Theory: Advances and Applications, 293)
Librería: California Books, Miami, FL, Estados Unidos de America
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Spectral Geometry of Graphs
Librería: GreatBookPricesUK, Woodford Green, Reino Unido
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Condición: New. Nº de ref. del artículo: 46844160-n
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Spectral Geometry of Graphs
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Spectral Geometry of Graphs
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Condición: As New. Unread book in perfect condition. Nº de ref. del artículo: 46844160
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Spectral Geometry of Graphs
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Condición: New. Nº de ref. del artículo: 26396996781
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Spectral Geometry of Graphs
Librería: GreatBookPricesUK, Woodford Green, Reino Unido
Calificación del vendedor: 5 de 5 estrellas
Condición: As New. Unread book in perfect condition. Nº de ref. del artículo: 46844160
Cantidad disponible: Más de 20 disponibles