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

Korányi, A.; Taylor, J. C.

doi:10.1090/S0002-9939-1985-0784178-8

Minimal solutions of the heat equation and uniqueness of the positive Cauchy problem on homogeneous spaces
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by A. Korányi and J. C. Taylor PDF

Proc. Amer. Math. Soc. 94 (1985), 273-278 Request permission

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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