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Product formula for resolvents of normal operators and the modified Feynman integral. (English) Zbl 0718.47023
In the series of papers [see for example, J. Funct. Anal. 63, 261-275 (1985; Zbl 0601.47025)], M. L. Lapidus developed the theory of the “modified Feynman integral” for Schrödinger operators in terms of Trotter-like product formula using the imaginary resolvents of the intervening operators. The aim of the reviewed paper is to extend this theory to the case of Schrödinger operators \(H=-(\nabla -ia)^ 2+V\) (a is a real vector potential) with highly singular complex potentials V. Both semigroups \(e^{-itH}\) and \(e^{-tH}\) corresponding to the dissipative systems or Nelson approach to Feynman integral respectively are studied.
Reviewer: R.Alicki (Gdańsk)

47D06 One-parameter semigroups and linear evolution equations
47L90 Applications of operator algebras to the sciences
81S40 Path integrals in quantum mechanics
28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
47B44 Linear accretive operators, dissipative operators, etc.
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