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.
Citation:
D. Schenk, M. A. Shubin, “Asymptotic expansion of the state density and the spectral function of a Hill operator”, Math. USSR-Sb., 56:2 (1987), 473–490
\Bibitem{SchShu85}
\by D.~Schenk, M.~A.~Shubin
\paper Asymptotic expansion of the state density and the spectral function of a~Hill operator
\jour Math. USSR-Sb.
\yr 1987
\vol 56
\issue 2
\pages 473--490
\mathnet{http://mi.mathnet.ru/eng/sm2178}
\crossref{https://doi.org/10.1070/SM1987v056n02ABEH003047}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=820398}
\zmath{https://zbmath.org/?q=an:0624.34018|0604.34015}
Linking options:
https://www.mathnet.ru/eng/sm2178
https://doi.org/10.1070/SM1987v056n02ABEH003047
https://www.mathnet.ru/eng/sm/v170/i4/p474
This publication is cited in the following 12 articles:
H. Boumaza, O. Lafitte, “Integrated density of states: From the finite range to the periodic Airy–Schrödinger operator”, Journal of Mathematical Physics, 62:4 (2021)
M. Braverman, V. M. Buchstaber, M. Gromov, V. Ivrii, Yu. A. Kordyukov, P. Kuchment, V. Maz'ya, S. P. Novikov, T. Sunada, L. Friedlander, A. G. Khovanskii, “Mikhail Aleksandrovich Shubin (obituary)”, Russian Math. Surveys, 75:6 (2020), 1143–1152
Leonid Parnovski, Roman Shterenberg, “Complete asymptotic expansion of the spectral function of multidimensional almost-periodic Schrödinger operators”, Duke Math. J., 165:3 (2016)
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
Yulia Karpeshina, Young-Ran Lee, “Spectral properties of a limit-periodic Schrödinger operator in dimension two”, JAMA, 120:1 (2013), 1
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
Schwarzenberger F., “Uniform Approximation of the Integrated Density of States for Long-Range Percolation Hamiltonians”, J. Stat. Phys., 146:6 (2012), 1156–1183
Leonid Parnovski, Roman Shterenberg, “Asymptotic expansion of the integrated density of states of a two-dimensional periodic Schrödinger operator”, Invent math, 2008
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
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
Yu. V. Egorov, M. A. Shubin, Encyclopaedia of Mathematical Sciences, 31, Partial Differential Equations II, 1994, 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
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