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.
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