Complete Modified Logarithmic Sobolev inequality for sub-Laplacian on $SU(2)$

Li Gao; Maria Gordina

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arXiv · 2203.12731

Complete Modified Logarithmic Sobolev inequality for sub-Laplacian on $SU(2)$

Li Gao·Maria Gordina

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Abstract

We prove that the canonical sub-Laplacian on $SU(2)$ admits a uniform modified log-Sobolev inequality for all its matrix-valued functions, independent of the matrix dimension. This is the first example of sub-Laplacian that a matrix-valued modified log-Sobolev inequality has been obtained. We also show that on Lie groups, the heat kernel measure $p_t$ at time $t$ admits matrix-valued modified log-Sobolev constants of order $O(t^{-1})$.

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Li Gao, Maria Gordina. 2022-03-23. Complete Modified Logarithmic Sobolev inequality for sub-Laplacian on $SU(2)$. https://arxiv.org/abs/2203.12731

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