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Weyl—Titchmarsh-type formula for periodic Schrödinger operator with Wigner—von Neumann potential

Published online by Cambridge University Press:  18 March 2013

Pavel Kurasov  and
Sergey Simonov
Pavel Kurasov
Affiliation:
Department of Mathematics, Lund Institute of Technology, 221 00 Lund, Sweden (kurasov@maths.lth.se)
Sergey Simonov
Affiliation:
Department of Mathematical Physics, Institute of Physics, St. Petersburg University, 1 Ulianovskaia, Peterhof 198904, St. Petersburg, Russia (sergey simonov@mail.ru)
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Abstract

The Schrödinger operator on the half-line with periodic background potential perturbed by a certain potential of Wigner—von Neumann type is considered. The asymptotics of generalized eigenvectors for λ ϵ ℂ+ and on the absolutely continuous spectrum is established. The Weyl—Titchmarsh-type formula for this operator is proven.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 2 , April 2013 , pp. 401 - 425
Copyright
Copyright © Royal Society of Edinburgh 2013

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