Mean value properties of the Laplacian via spectral theory
Author:
Robert S. Strichartz
Journal:
Trans. Amer. Math. Soc. 284 (1984), 219-228
MSC:
Primary 31C12; Secondary 22E30, 35P99, 43A85
DOI:
https://doi.org/10.1090/S0002-9947-1984-0742422-0
MathSciNet review:
742422
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be an even entire function of temperate exponential type,
a selfadjoint realization of
, where
is the Laplace-Beltrami operator on a Riemannian manifold, and
the operator given by spectral theory. A Paley-Wiener theorem on the support of
is proved, and is used to show that
on a suitable domain implies
, as well as a generalization of Àsgeirsson's theorem. A concrete realization of the operators
is given in the case of a compact Lie group or a noncompact symmetric space with complex isometry group.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1984-0742422-0
Keywords:
Laplace-Beltrami operator,
spectral theory,
mean value theorem,
Asgeirsson's theorem,
functions of the Laplacian,
Paley-Wiener theorem,
symmetric space,
compact Lie group
Article copyright:
© Copyright 1984
American Mathematical Society