Abstract:
The problem Au=tBu is considered in a bounded Lipschitz domain, where A and are sums of a pseudodifferential operator satisfying a transmission condition and a singular Green operator, with A elliptic. Under natural conditions the classical formula for the asymptotics of the spectrum is established, with an estimate of the remainder determined by the character of degeneration in ellipticity of the operator B.
Bibliography: 18 titles.
\Bibitem{Lev84}
\by S.~Z.~Levendorskii
\paper Asymptotics of the spectrum of linear operator pencils
\jour Math. USSR-Sb.
\yr 1985
\vol 52
\issue 1
\pages 245--266
\mathnet{http://mi.mathnet.ru/eng/sm2050}
\crossref{https://doi.org/10.1070/SM1985v052n01ABEH002887}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=746070}
\zmath{https://zbmath.org/?q=an:0571.35081|0553.35067}
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https://www.mathnet.ru/eng/sm2050
https://doi.org/10.1070/SM1985v052n01ABEH002887
https://www.mathnet.ru/eng/sm/v166/i2/p251
This publication is cited in the following 6 articles:
Mark S. Ashbaugh, Fritz Gesztesy, Marius Mitrea, Roman Shterenberg, Gerald Teschl, Operator Theory: Advances and Applications, 232, Mathematical Physics, Spectral Theory and Stochastic Analysis, 2013, 1
Mark S. Ashbaugh, Fritz Gesztesy, Marius Mitrea, Gerald Teschl, “Spectral theory for perturbed Krein Laplacians in nonsmooth domains”, Advances in Mathematics, 223:4 (2010), 1372
K. Kh. Boimatov, “Asymptotics of spectral projectors of pseudodifferential operators”, Funct. Anal. Appl., 26:1 (1992), 42–44
S. Z. Levendorskii, “Asymptotics of the spectrum of problems with constraints”, Math. USSR-Sb., 57:1 (1987), 77–95
Citation in format AMSBIB
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