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 Mat. Sb. (N.S.), 1985, Volume 128(170), Number 4(12), Pages 474–491 (Mi msb2178)

This article is cited in 8 scientific papers (total in 8 papers)

Asymptotic expansion of the state density and the spectral function of a Hill operator

D. Schenk, M. A. Shubin

Abstract: Complete asymptotic expansions are obtained for the integrated state density and the spectral function of a Hill operator with smooth potential. These expansions can be differentiated any number of times outside small neighborhoods of forbidden zones.
Bibliography: 18 titles.

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English version:
Mathematics of the USSR-Sbornik, 1987, 56:2, 473–490

Bibliographic databases:

UDC: 517.984.5
MSC: Primary 34B25, 34B30, 34E05; Secondary 35J10, 70H99
Received: 24.07.1984

Citation: D. Schenk, M. A. Shubin, “Asymptotic expansion of the state density and the spectral function of a Hill operator”, Mat. Sb. (N.S.), 128(170):4(12) (1985), 474–491; Math. USSR-Sb., 56:2 (1987), 473–490

Citation in format AMSBIB
\Bibitem{SchShu85} \by D.~Schenk, M.~A.~Shubin \paper Asymptotic expansion of the state density and the spectral function of a~Hill operator \jour Mat. Sb. (N.S.) \yr 1985 \vol 128(170) \issue 4(12) \pages 474--491 \mathnet{http://mi.mathnet.ru/msb2178} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=820398} \zmath{https://zbmath.org/?q=an:0624.34018|0604.34015} \transl \jour Math. USSR-Sb. \yr 1987 \vol 56 \issue 2 \pages 473--490 \crossref{https://doi.org/10.1070/SM1987v056n02ABEH003047} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Volovoy A., “Improved 2-Term Asymptotics for the Eigenvalue Distribution Function of an Elliptic Operator on a Compact Manifold”, Commun. Partial Differ. Equ., 15:11 (1990), 1509–1563
2. Ilin V., Antoniou I., “On the Uniform Equiconvergence with the Fourier Integral, on the Whole Line R, for an Arbitrary l(P)(R) Function, of the Spectral Expansion Related to the Selfadjoint Extension of the Hill Operator”, Differ. Equ., 31:8 (1995), 1253–1266
3. Antoniou I. Ilin V., “The Uniform, Over the Whole Line R Estimates of Spectral Expansions Related to the Selfadjoint Extensions of the Hill Operator and of the Schrodinger Operator with a Bounded and Measurable Potential”, Comput. Math. Appl., 34:5-6 (1997), 627–632
4. Leonid Parnovski, Roman Shterenberg, “Asymptotic expansion of the integrated density of states of a two-dimensional periodic Schrödinger operator”, Invent math, 2008
5. Leonid Parnovski, Roman Shterenberg, “Complete asymptotic expansion of the integrated density of states of multidimensional almost-periodic Schrödinger operators”, Ann. Math, 176:2 (2012), 1039
6. Schwarzenberger F., “Uniform Approximation of the Integrated Density of States for Long-Range Percolation Hamiltonians”, J. Stat. Phys., 146:6 (2012), 1156–1183
7. Sergey Morozov, Leonid Parnovski, Roman Shterenberg, “Complete Asymptotic Expansion of the Integrated Density of States of Multidimensional Almost-Periodic Pseudo-Differential Operators”, Ann. Henri Poincaré, 2013
8. Yulia Karpeshina, Young-Ran Lee, “Spectral properties of a limit-periodic Schrödinger operator in dimension two”, JAMA, 120:1 (2013), 1
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