Introduction to Maslov’s operational method (non-commutative analysis and differential equations). (English. Russian original) Zbl 0816.58037

Global analysis, studies and applications. V. Lect. Notes Math. 1520, 81-91 (1992); translation from Algebraicheskie voprosy analiza i topologii, Nov. Global. Anal. 1990, 52-60 (1990).
The authors give an introduction to Maslov’s method of noncommutative analysis. It is explained how to define a function of several noncommuting operators using Feynman’s convention. An application to an algebra of operators \(\{f(\overset {1} {A}_ 1,\dots,\overset {n} {A}_ n)\}\) in the case when the commutators \([A_ j,A_ k]\) are linear functions of \(\{A_ i\}\) is considered as well.
For the entire collection see [Zbl 0779.00007].


58J40 Pseudodifferential and Fourier integral operators on manifolds
47G30 Pseudodifferential operators