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Proceedings of the American Mathematical Society

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

 
 

 

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.


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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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