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INTERNATIONAL JOURNAL OF ISSN 1312-7586 (print) ISSN 1314-7544 (online) |
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O. A. Veliev Perturbation theory for the periodic multidimensional Schrodinger operator and the Bethe-Sommerfeld conjecture Int. Journal of Contemp. Math. Sciences, Vol. 2, 2007, no. 1-4, 19-87 http://dx.doi.org/10.12988/ijcms.2007.07003 Copyright © 2007 O. A. Veliev. This article is distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Cited by (11): Sedef Karakilic and Setenay Akduman, Eigenvalue asymptotics for the Schrodinger operator with a matrix potential in a single resonance domain, Filomat, 29 (2015), no. 1, 21-38 [CrossRef] Oktay Veliev, Asymptotic Formulas for the Bloch Eigenvalues and Bloch Functions, Chapter in Multidimensional Periodic Schrodinger Operator, Springer International Publishing, 2015, 31-126 [CrossRef] Irina Pchelintseva, Spectral Properties of Periodic Pseudo-differential Operators, Diss., University College London, 2012 [View at Publisher] Oktay A. Veliev, An algorithm for finding the periodic potential of the three-dimensional Schrodinger operator from spectral invariants, Journal of Physics A: Mathematical and Theoretical, 44 (2011), no. 15 [CrossRef] Didem Coskan and Sedef Karakilic, High energy asymptotics for eigenvalues of the Schrodinger operator with a matrix potential, Mathematical Communications, 16 (2011), no. 2, 551-567 [View at Publisher] Leonid Parnovski and Alexander V. Sobolev, Bethe-Sommerfeld conjecture for periodic operators with strong perturbations, Inventiones Mathematicae, 181 (2010), no. 3, 467-540 [CrossRef] G. Barbatis and L. Parnovski, Bethe-Sommerfeld Conjecture for Pseudodifferential Perturbation, Communications in Partial Differential Equations, 34 (2009), no. 4, 383-418 [CrossRef] O. A. Veliev, On the constructive determination of the periodic potentials from the Bloch eigenvalues, Journal of Physics A: Mathematical and Theoretical, 42 (2009), no. 37 [CrossRef] Leonid Parnovski, Bethe-Sommerfeld conjecture, Annales Henri Poincare, 9 (2008), no. 3, 457-508 [CrossRef] Yulia Karpeshina and Young-Ran Lee, Absolutely continuous spectrum of a polyharmonic operator with a limit periodic potential in dimension two, Communications in Partial Differential Equations, 33 (2008), no. 9, 1711-1728 [CrossRef] Oktay A. Veliev, On the constructive determination of spectral invariants of the periodic Schrodinger operator with smooth potentials, Journal of Physics A: Mathematical and Theoretical, 41 (2008), no. 36 [CrossRef]
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