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L. Saloff-Coste 《Potential Analysis》1995,4(4):429-467
Old and recent results concerning Harnack inequalities for divergence form operators are reviewed. In particular, the characterization of the parabolic Harnack principle by simple geometric properties -Poincaré inequality and doubling property- is discussed at length. It is shown that these two properties suffice to apply Moser's iterative technique. 相似文献
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We study the rate of convergence of symmetric random walks on finite groups to the uniform distribution. A notion of moderate growth is introduced that combines with eigenvalue techniques to give sharp results. Roughly, for finite groups of moderate growth, a random walk supported on a set of generators such that the diameter of the group is requires order 2 steps to get close to the uniform distribution. This result holds for nilpotent groups with constants depending only on the number of generators and the class. Using Gromov's theorem we show that groups with polynomial growth have moderate growth. 相似文献
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Laurent Saloff-Coste 《Arkiv f?r Matematik》1990,28(1-2):315-331
From Gaussian upper bounds on the heat kernel we deduce similar upper bounds on the first space derivatives of the heat kernel. Gaussian lower bounds on the heat kernel are deduced and some applications are given. 相似文献
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An inequality for superharmonic functions on Riemannian manifolds due to S.Y. Cheng and S-T. Yau is adapted to the setting of graphs. A number of corollaries are discussed, including a Harnack inequality for graphs having at most quadratic growth and satisfying a certain connectedness condition. 相似文献
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Sans résumé
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Given a self-adjoint semigroup e−tA
satisfying an ultracontractivity bound of the type , we find conditions on the sequence that imply that f is a bounded function. Sobolev’s classical embedding theorem says that, when A is the Laplace operator on , for some k > d/4 suffices to imply that f is bounded. In the cases we are interested in, the desired condition involves the whole sequence and depends on the behavior of the ultracontractivity function m.
Research of A. Bendikov was supported by the Polish Goverment Scientific Research Fund, Grant 1 PO3 A 03129. Research of T.
Coulhon was partially supported by the European Commission (IHP Network “Harmonic Analysis and Related Problems” 2002–2006,
Contract HPRN-CT-2001-00273-HARP). Research of L. Saloff-Coste was partially supported by NSF grant DMS-0102126. 相似文献
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Laurent Saloff-Coste 《Milan Journal of Mathematics》1995,65(1):139-158
Borrowing ideas from a work of S.Y. Cheng and S-T. Yau, we prove a number of inequalities for positivep-superharmonic functions on networks.
Conferenza tenuta l'1 giugno 1995 相似文献
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