Spectral Geometry of Graphs
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....
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Springer Berlin Heidelberg
2024
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=nlebk&AN=3730110&site=ehost-live header: @attributes: shortDbName: nlebk uiTerm: 3730110 longDbName: eBook Collection (EBSCOhost) uiTag: AN controlInfo: bkinfo: btl: Spectral Geometry of Graphs aug: au: Pavel Kurasov sertl: Operator Theory: Advances and Applications isbn: 9783662678701 9783662678725 imageinfo: pubinfo: dt: @attributes: year: 2024 month: 01 day: 01 dtAvail: @attributes: year: 2024 month: 09 day: 06 vid: 00293 pub: Springer Berlin Heidelberg pubContract: Springer Nature place: Berlin price: 0.01 limitsGroup: maxCheckoutDays: 1500 copyPages: 10 pda: N printPagesOffline: 10 printPagesOnline: 10 previewPages: 0 prePubGroup: dewey: @attributes: class: 515.7242 item: 515 .7242 lc: @attributes: class: QA329.4 item: QA 329 .4 artinfo: ui: 3730110 1409334828 formats: fmt: – @attributes: type: EB doid: NL$3730110$PDF caption: PDF download: Y – @attributes: type: EK doid: NL$3730110$EPUB caption: EPUB download: Y tig: atl: Spectral Geometry of Graphs ptl: Spectral Geometry of Graphs aug: au: Pavel Kurasov su: Differential operators Spectral theory (Mathematics) Graphic methods sug: subj: COMPUTERS / Quantum Computing MATHEMATICS / Mathematical Analysis SCIENCE / System Theory MATHEMATICS / Optimization Differential operators Spectral theory (Mathematics) Graphic methods ab: 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. pubtype: eBook doctype: Book ougenre: Book language: English copyright: @attributes: flag: N copyrightText: holdings: @attributes: islocal: N |
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