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000913216 019__ $$a1117304004$$a1117703886$$a1119615868$$a1120970896
000913216 020__ $$a9783030245788$$q(electronic book)
000913216 020__ $$a3030245780$$q(electronic book)
000913216 0248_ $$a10.1007/978-3-030-24
000913216 035__ $$aSP(OCoLC)on1111982638
000913216 035__ $$aSP(OCoLC)1111982638$$z(OCoLC)1117304004$$z(OCoLC)1117703886$$z(OCoLC)1119615868$$z(OCoLC)1120970896
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000913216 049__ $$aISEA
000913216 050_4 $$aQC174.17.S3$$bV45 2019
000913216 08204 $$a530.12/4$$223
000913216 1001_ $$aVeliev, Oktay,$$eauthor.
000913216 24510 $$aMultidimensional periodic Schrödinger operator :$$bperturbation theory and applications /$$cOktay Veliev.
000913216 250__ $$aSecond edition.
000913216 264_1 $$aCham, Switzerland :$$bSpringer,$$c[2019]
000913216 300__ $$a1 online resource (333 pages)
000913216 336__ $$atext$$btxt$$2rdacontent
000913216 337__ $$acomputer$$bc$$2rdamedia
000913216 338__ $$aonline resource$$bcr$$2rdacarrier
000913216 504__ $$aIncludes bibliographical references and index.
000913216 506__ $$aAccess limited to authorized users.
000913216 520__ $$aThis book describes the direct and inverse problems of the multidimensional Schrödinger operator with a periodic potential, a topic that is especially important in perturbation theory, constructive determination of spectral invariants and finding the periodic potential from the given Bloch eigenvalues. It provides a detailed derivation of the asymptotic formulas for Bloch eigenvalues and Bloch functions in arbitrary dimensions while constructing and estimating the measure of the iso-energetic surfaces in the high-energy regime. Moreover, it presents a unique method proving the validity of the Bethe-Sommerfeld conjecture for arbitrary dimensions and arbitrary lattices. Using the perturbation theory constructed, it determines the spectral invariants of the multidimensional operator from the given Bloch eigenvalues. Some of these invariants are explicitly expressed by the Fourier coefficients of the potential, making it possible to determine the potential constructively using Bloch eigenvalues as input data. Lastly, the book presents an algorithm for the unique determination of the potential. This updated second edition includes an additional chapter that specifically focuses on lower-dimensional cases, providing the basis for the higher-dimensional considerations of the chapters that follow.
000913216 588__ $$aDescription based on online resource; title from digital title page (viewed on September 13, 2019).
000913216 650_0 $$aSchrödinger operator.
000913216 650_0 $$aPerturbation (Mathematics)
000913216 650_0 $$aSpectral theory (Mathematics)
000913216 77608 $$iPrint version:$$aVeliev, Oktay$$tMultidimensional Periodic Schrödinger Operator : Perturbation Theory and Applications$$dCham : Springer,c2019$$z9783030245771
000913216 852__ $$bebk
000913216 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-030-24578-8$$zOnline Access$$91397441.1
000913216 909CO $$ooai:library.usi.edu:913216$$pGLOBAL_SET
000913216 980__ $$aEBOOK
000913216 980__ $$aBIB
000913216 982__ $$aEbook
000913216 983__ $$aOnline
000913216 994__ $$a92$$bISE