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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Some spectral properties of the perturbed polyharmomic operator
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by Daniel Eidus PDF
Proc. Amer. Math. Soc. 96 (1986), 410-412 Request permission

Abstract:

We deal with the polyharmonic operator perturbed by a potential, decreasing at infinity as ${\left | x \right |^{ - \sigma }}$. Under some conditions we obtain the absence of eigenvalues in a neighbourhood of the point $z = 0$, the existence of the strong limit and the asymptotic expansion of the corresponding resolvent ${R_z}$, considered in weighted ${L^2}$-spaces, as $z \to 0$, where $z$ is the spectral parameter.
References
  • Daniel Eidus, Solutions of external boundary problems for small values of the spectral parameter, Integral Equations Operator Theory 9 (1986), no. 1, 47–59. MR 824619, DOI 10.1007/BF01257061
  • Minoru Murata, Asymptotic expansions in time for solutions of Schrödinger-type equations, J. Funct. Anal. 49 (1982), no. 1, 10–56. MR 680855, DOI 10.1016/0022-1236(82)90084-2
  • B. R. Vainberg, On exterior elliptic problems polynomially depending on a spectral parameter, Mat. Sb. 21 (1973), 221-239.
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 96 (1986), 410-412
  • MSC: Primary 35J30; Secondary 35P05
  • DOI: https://doi.org/10.1090/S0002-9939-1986-0822430-9
  • MathSciNet review: 822430