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arXiv · 1608.01869

Surjectivity of Mean Value Operators on Noncompact Symmetric Spaces

Jens Christensen·Fulton Gonzalez·Tomoyuki Kakehi
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Abstract

Let $X=G/K$ be a symmetric space of the non-compact type. We prove that the mean value operator over translated $K$-orbits of a fixed point is surjective on the space of smooth functions on $X$ if $X$ is either complex or of rank one. For higher rank spaces it is shown that the same statement is true for points in an appropriate Weyl subchamber.

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Jens Christensen, Fulton Gonzalez, Tomoyuki Kakehi. 2016-08-05. Surjectivity of Mean Value Operators on Noncompact Symmetric Spaces. https://arxiv.org/abs/1608.01869

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