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The moments of certain complex potentials


Authors: Howard D. Fegan and Peter B. Gilkey
Journal: Proc. Amer. Math. Soc. 96 (1986), 525-527
MSC: Primary 58G25; Secondary 58G11
DOI: https://doi.org/10.1090/S0002-9939-1986-0822453-X
MathSciNet review: 822453
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Abstract: Let $ M$ be a compact homogeneous space, let $ \Delta $ be the Laplacian, and let $ V$ be the vector space of Fegan potentials. If $ q \in V$, then $ \Delta $ and $ \Delta + q$ have the same spectrum. We show that all the moments of such a potential must vanish.


References [Enhancements On Off] (What's this?)

  • [1] P. Gilkey, Recursion relations and the asymptotic behavior of the eigenvalues of the Laplacian, Compositio Math. 38 (1979), 201-240. MR 528840 (80i:53020)
  • [2] V. Guillemin and A. Uribe, Spectral properties of a certain class of complex potentials, Trans. Amer. Math. Soc. 279 (1983), 759-771. MR 709582 (84j:58129)

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DOI: https://doi.org/10.1090/S0002-9939-1986-0822453-X
Article copyright: © Copyright 1986 American Mathematical Society

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