A representation of the solutions of the Darboux equation in odd-dimensional spaces
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- by H. Rhee PDF
- Trans. Amer. Math. Soc. 150 (1970), 491-498 Request permission
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.References
- Y. W. Chen, On the solutions of the wave equation in the exterior of the characteristic cones, J. Math. Mech. 16 (1967), 655–673. MR 0212418
- Fritz John, Plane waves and spherical means applied to partial differential equations, Interscience Publishers, New York-London, 1955. MR 0075429
- Fritz John, Bestimmung einer Funktion aus ihren Integralen Über gewisse Mannigfaltigkeiten, Math. Ann. 109 (1934), no. 1, 488–520 (German). MR 1512906, DOI 10.1007/BF01449151 H. Rhee, Inversion of the functional equation ${\text {SM} ^ \ast }f = J$ in odd-dimensional spaces, Thesis, Univ. of Massachusetts, Amherst, 1968.
Additional Information
- © Copyright 1970 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 150 (1970), 491-498
- MSC: Primary 35.06
- DOI: https://doi.org/10.1090/S0002-9947-1970-0262647-0
- MathSciNet review: 0262647