Gaugeability and conditional gaugeability

被引:90
作者
Chen, ZQ [1 ]
机构
[1] Univ Washington, Dept Math, Seattle, WA 98195 USA
关键词
Green function; h-transform; conditional Markov process; lifetime; time change; Kato class; Feynman-Kac transform; Schrodinger semigroup; Stieltjes exponential; non-local perturbation; spectral radius; gauge theorem; conditional gauge theorem; super gauge theorem; super conditional gauge theorem; subcriticality; bilinear form;
D O I
10.1090/S0002-9947-02-03059-3
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
New Kato classes are introduced for general transient Borel right processes, for which gauge and conditional gauge theorems hold. These new classes are the genuine extensions of the Green-tight measures in the classical Brownian motion case. However, the main focus of this paper is on establishing various equivalent conditions and consequences of gaugeability and conditional gaugeability. We show that gaugeability, conditional gaugeability and the subcriticality for the associated Schrodinger operators are equivalent for transient Borel right processes with strong duals. Analytic characterizations of gaugeability and conditional gaugeability are given for general symmetric Markov processes. These analytic characterizations are very useful in determining whether process perturbed by potential is gaugeable or conditionally gaugeable in concrete cases. Connections with the positivity of the spectral radii of the associated Schrodinger operators are also established.
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页码:4639 / 4679
页数:41
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