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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A representation of the solutions of the Darboux equation in odd-dimensional spaces


Author: H. Rhee
Journal: Trans. Amer. Math. Soc. 150 (1970), 491-498
MSC: Primary 35.06
MathSciNet review: 0262647
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Abstract: It is shown that determining a function from its averages over all spheres passing through the origin leads to an explicit representation of the even solutions of the Darboux equation in the exterior of the characteristic cones in terms of the hyperboloidal means of the boundary data on the cones.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1970-0262647-0
PII: S 0002-9947(1970)0262647-0
Keywords: Darboux equation, characteristic cones, spherical means, hyperboloidal means, John-Asgeiersson identity, Radon transform
Article copyright: © Copyright 1970 American Mathematical Society