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On estimating the hypercontractive constant of a diffusion process on a compact manifold. (English) Zbl 0743.60075

Diffusion processes and related problems in analysis, Vol. I: Diffusions in analysis and geometry, Proc. Int. Conf., Evanston/IL (USA) 1989, Prog. Probab. 22, 149-154 (1990).
[For the entire collection see Zbl 0716.00011.]
Let \(M\) be an \(N\)-dimensional, connected, compact \(C^ \infty\) Riemannian manifold. \(\{P_ t, t>0\}\) denotes the Markov semigroup, connected with the solution of the martingale problem for \(\Delta\) on \(C^ \infty(M)\) at \(x,x\in M\), where \(\Delta\) is the Laplacian. Some estimates of the hypercontractive constant of \(\{P_ t, t>0\}\) are given in terms of the geometry of \(M\).
Reviewer: Wu Rong (Tianjin)

MSC:

60J60 Diffusion processes
47D07 Markov semigroups and applications to diffusion processes

Citations:

Zbl 0716.00011
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