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Feynman’s operational calculi for time dependent noncommuting operators. (English) Zbl 0984.47013

A comprehensive discussion concerning the classical construction of R. Feynman concerning the operational calculus can be found in the recent monograph “The Feynman integral and Feynman’s operational calculus” by G. W. Johnson and M. L. Lapidus dedicated to this subject (see Zbl 0952.46044). In the present paper, the authors study Feynman’s operational calculus for operator-valued functions of time and for measures which are not necessarily probability measures. The so called disentangling map is related to the solutions of evolution equations, and the presence of some unbounded operators is allowed.

MSC:

47A60 Functional calculus for linear operators
46T12 Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds
47N50 Applications of operator theory in the physical sciences
28A33 Spaces of measures, convergence of measures
28A25 Integration with respect to measures and other set functions
47A56 Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces

Citations:

Zbl 0952.46044
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