{"product_id":"9783662678701","title":"Operator Theory: Advances and Applications","description":"\u003ch1\u003eOperator Theory: Advances and Applications\u003c\/h1\u003e \u003ch2\u003eKurasov, Pavel\u003c\/h2\u003e \u003cp\u003eThis 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.\u003c\/p\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003eThe book has two central themes: the \u003cb\u003etrace formula\u003c\/b\u003e and \u003cb\u003einverse problems\u003c\/b\u003e.\u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003eThe \u003cb\u003etrace formula\u003c\/b\u003e 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.\u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003eTo solve the \u003cb\u003einverse problem\u003c\/b\u003e 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.\u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003eThe 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.\u003cdiv\u003e\u003cp\u003e\u003c\/p\u003e\u003c\/div\u003e\n\u003c\/div\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Birkhäuser\u003c\/p\u003e \u003cp\u003ePublication Date: 2023-11-09\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9783662678701\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-662-67872-5\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 639\u003c\/p\u003e ","brand":"Springer Berlin Heidelberg","offers":[{"title":"Default Title","offer_id":44398491173004,"sku":"9783662678701","price":53.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783662678701.jpg?v=1775680973","url":"https:\/\/lateknightbooks.com\/products\/9783662678701","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}