An Estimate of the Gap of Spectrum of Schrödinger Operators which Generate Hyperbounded Semigroups

作者: Shigeki Aida

DOI: 10.1006/JFAN.2001.3774

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摘要: Abstract Logarithmic Sobolev inequalities with potential functions on loop spaces were proved by L. Gross (1991, J. Funct. Anal. 102 , 265–313), S. Aida (1996, in “Proceedings of the Fifth Gregynog Symposium, Stochastic Analysis and Applications,” pp. 1–19, World Scientific, Singapore), F.-Z. Gong Z.-M. Ma (1998, 599–623). The generators Dirichlet forms are Schrodinger operators they generate hyperbounded semigroups. Recently, Gong, M. Rockner Wu (2000, Poincare inequality for weighted first order spaces, submitted) existence gap spectrum at lowest eigenvalue using Hino's exponential decay estimates semigroup Osaka Math. 37 603–624) author's strong ergodicity property semi-group (S. Aida, 1998, 158 152–185). In this paper, we will give a lower bound weak which was introduced F.-Y. Wang Weak L 2 -convergence rates Markov semigroups, preprint). Also distribution function ground states inequality.

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