Feynman measure in the phase space and symbols of infinite-dimensional pseudodifferential operators
type: Item
instance of: scholarly article
title: Feynman measure in the phase space and symbols of infinite-dimensional pseudodifferential operators
zbMATH Open document ID: 0607.35090
DOI: 10.1007/BF01157974
published in: Mathematical Notes
publication date: 1985-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 28C20
Mathematics Subject Classification ID: 70G10
zbMATH DE Number: 3981713
zbMATH Keywords: Keller's convergence structure
zbMATH Keywords: Feynman measure
zbMATH Keywords: phase space
zbMATH Keywords: algebra
zbMATH Keywords: infinite dimensional pseudo-differential operators
zbMATH Keywords: polynomial symbols
author: Andrei Khrennikov
reviewed by: Akira Tsutsumi
MaRDI profile type: Publication
cites work: Q3317511
cites work: Q3337807
cites work: Q3995048
cites work: Q3854176
cites work: Q5516366
cites work: MEASURES ON LINEAR TOPOLOGICAL SPACES
cites work: Q5736344
description: scientific article; zbMATH DE number 3981713