Physics – Mathematical Physics
Scientific paper
2005-12-22
Journal of Functional Analysis 102 (1991) No 2, 414--447
Physics
Mathematical Physics
28 pages. See also related papers at http://www.maths.nott.ac.uk/personal/vpb/research/ana_cal.html and http://www.maths.not
Scientific paper
A generalized definition of quantum stochastic (QS) integrals and differentials is given in the free of adaptiveness and basis form in terms of Malliavin derivative on a projective Fock scale, and their uniform continuity and QS differentiability with respect to the inductive limit convergence is proved. A new form of QS calculus based on an inductive *-algebraic structure in an indefinite space is developed and a nonadaptive generalization of the QS Ito formula for its representation in Fock space is derived. The problem of solution of general QS evolution equations in a Hilbert space is solved in terms of the constructed operator representation of chronological products, defined in the indefinite space, and the unitary and *-homomorphism property respectively for operators and maps of these solutions, corresponding to the pseudounitary and *-homomorphism property of the QS integrable generators, is proved.
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