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Proceedings of the American Mathematical Society

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Minimal solutions of the heat equation and uniqueness of the positive Cauchy problem on homogeneous spaces


Authors: A. Korányi and J. C. Taylor
Journal: Proc. Amer. Math. Soc. 94 (1985), 273-278
MSC: Primary 58G11; Secondary 35K05, 43A85
DOI: https://doi.org/10.1090/S0002-9939-1985-0784178-8
MathSciNet review: 784178
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Abstract: The minimal positive solutions of the heat equation on $ X \times ( - \infty ,T)$ are determined for $ X$ a homogeneous Riemannian space. A simple proof of uniqueness for the positive Cauchy problem on a homogeneous space is given using Choquet's theorem and the explicit form of these solutions.


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DOI: https://doi.org/10.1090/S0002-9939-1985-0784178-8
Keywords: Heat equation, minimal solutions, Cauchy problem, homogeneous space, bounded geometry
Article copyright: © Copyright 1985 American Mathematical Society