The range of the heat operator

Details The range of the heat operator The range of the heat operator

2004-09-17

arxiv.org/abs/math/0409308v2

The Ubiquitous Heat Kernel, edited by Jay Jorgensen and Lynne Walling, AMS 2006, pp. 203-231

Mathematics

Differential Geometry

Final version. To appear in "The Ubiquitous Heat Kernel," edited by Jay Jorgenson and Lynne Walling

Scientific paper

This paper describes results characterizing the range of the time-t heat operator on various manifolds, including Euclidean spaces, spheres, and hyperbolic spaces. The guiding principle behind these results is this: The functions in the range of the heat operator should be, roughly, those functions having an analytic continuation to the appropriate complexified manifold with growth in the imaginary directions at most like that of the time-t heat heat kernel.

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