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A probabilistic principle and generalized Schrödinger perturbation. (English) Zbl 0748.60069

Summary: We present a probabilistic principle: for an additive functional of certain Markov processes, its smallness with time is equivalent to its smallness with space, and apply it to a perturbation problem for relativistic Schrödinger operators.

MSC:

60J55 Local time and additive functionals
60H25 Random operators and equations (aspects of stochastic analysis)
81Q15 Perturbation theories for operators and differential equations in quantum theory
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