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Some spectral properties of the perturbed polyharmomic operator


Author: Daniel Eidus
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
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Abstract: We deal with the polyharmonic operator perturbed by a potential, decreasing at infinity as $ {\left\vert x \right\vert^{ - \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 [Enhancements On Off] (What's this?)

  • [1] D. Eidus, Solutions of external boundary problems for small values of the spectral parameter, Integral Equations and Operator Theory 9 (1986), 21-32. MR 824619 (87j:47071)
  • [2] M. Murata, Asymptotic expansion in time for solutions of Schrödinger-type equations, J. Funct. Anal. 49 (1982), 10-56. MR 680855 (85d:35019)
  • [3] B. R. Vainberg, On exterior elliptic problems polynomially depending on a spectral parameter, Mat. Sb. 21 (1973), 221-239.

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DOI: https://doi.org/10.1090/S0002-9939-1986-0822430-9
Article copyright: © Copyright 1986 American Mathematical Society

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