Multidimensional Periodic Schrödinger Operator: Perturbation Theory and Applications - Rilegato

Veliev, Oktay

Rilegato

ISBN 10: 3030245772 ISBN 13: 9783030245771

Casa editrice: Springer Nature, 2019

Riassunto

This 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.

Su questo libro

Informazioni sull?autore

Oktay Veliev received his B.S. degree in Mathematics in 1977 and Ph.D. degree in Mathematics in 1980 from Moscow State University, earning a Doctor of Sciences degree in 1989. From 1980 to 1983, he was a researcher and then senior researcher (1983–1988) at the Institute of Mathematics of the Academy of Sciences of Azerbaijan SSR. At Baku State University (Azerbaijan) he has been an Associate Professor (1988–1991), a Professor (1991–1992), and Head of the Department of Functional Analysis (1992–1997). Between 1993 and 1997, he was President of the Azerbaijan Mathematical Society. He was a visiting Professor at the University of Nantes (France), the Institute of Mathematics at the ETH (Switzerland), and Sussex University (England). From 1997 to 2002 he was a Professor at Dokuz Eylul University (Turkey), and since 2003 has been a Professor at Dogus University (Turkey). He has received grants from the American Mathematical Society and the International Science Foundation (Grant No. MVVOOO).

Dalla quarta di copertina

This 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.

Dettagli dell?edizione

• Editore: Springer Nature
• Data di pubblicazione: 2019
• Lingua: Inglese
• ISBN 10: 3030245772
• ISBN 13: 9783030245771
• Rilegatura: Copertina rigida
• Numero edizione: 2
• Numero di pagine: 326
• Contatto del produttore: {language_tag:it_IT,value:"Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com"}