Feynman measure in the phase space and symbols of infinite-dimensional pseudodifferential operators
In the paper by the author, ''Some applications of Keller's convergence structure to the nonlinear functional analysis'' [Abh. Akad. Wiss. DDR, Abt. Math., Naturwiss. Tech. 1984, No.2N, 113-117 (1984)] the Feynman measure on locally convex space was defined. The author extends the definition to the Feynman measure on the phase space. And for the measure he constructs an algebra of infinite dimensional pseudo-differential operators, which contains, in particular, all the Ps.D. Ops. with polynomial symbols. He gives a formula expressing the symbol of the composition of two Ps.D.Ops. through their symbols, and a formula relating the pq- and qp-symbols is also given.
infinite dimensional pseudo-differential operators
scientific article; zbMATH DE number 3981713