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Spectral Geometry of Graphs (Operator Theory: Advances and Applications, 293) free ebook download

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Mathematics

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Author(s):	Pavel Kurasov

Date:	2023	Format:	pdf	Language:	English	ISBN/ASIN:	3662678705
Pages:	655	OCR:		Quality:		ISBN13:	9783662678701
Uploader:	G0mer	Upload Date:	2/8/2024 4:38:56 PM

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3662678705 pdf
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 Schrodinger 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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3232980	Download	https://nitroflare.com/view/B4EEA455B68A...		7.00	G0mer

Tags: Advances Applications Geometry Graphs Operator Spectral Theory

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Spectral Geometry of Graphs (Operator Theory: Advances and Applications, 293) free ebook download

Category: Mathematics

Description: Click to see full description

Category:
Mathematics