The moments of certain complex potentials

Fegan, Howard D.; Gilkey, Peter B.

doi:10.1090/S0002-9939-1986-0822453-X

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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The moments of certain complex potentials
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by Howard D. Fegan and Peter B. Gilkey PDF

Proc. Amer. Math. Soc. 96 (1986), 525-527 Request permission

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

Peter B. Gilkey, Recursion relations and the asymptotic behavior of the eigenvalues of the Laplacian, Compositio Math. 38 (1979), no. 2, 201–240. MR 528840
V. Guillemin and A. Uribe, Spectral properties of a certain class of complex potentials, Trans. Amer. Math. Soc. 279 (1983), no. 2, 759–771. MR 709582, DOI 10.1090/S0002-9947-1983-0709582-8