Spectral Geometry of Graphs is popular PDF and ePub book, written by Pavel Kurasov in 2023-12-09, it is a fantastic choice for those who relish reading online the Science genre. Let's immerse ourselves in this engaging Science book by exploring the summary and details provided below. Remember, Spectral Geometry of Graphs can be Read Online from any device for your convenience.
Spectral Geometry of Graphs Book PDF Summary
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.
Detail Book of Spectral Geometry of Graphs PDF
- Author : Pavel Kurasov
- Release : 09 December 2023
- Publisher : Springer Nature
- ISBN : 9783662678725
- Genre : Science
- Total Page : 644 pages
- Language : English
- PDF File Size : 18,7 Mb
If you're still pondering over how to secure a PDF or EPUB version of the book Spectral Geometry of Graphs by Pavel Kurasov, don't worry! All you have to do is click the 'Get Book' buttons below to kick off your Download or Read Online journey. Just a friendly reminder: we don't upload or host the files ourselves.