Time dependent stability for Feynman's operational calculus
type: Item
instance of: scholarly article
title: Time dependent stability for Feynman's operational calculus
zbMATH Open document ID: 1101.47011
author: Lance Nielsen
published in: Rocky Mountain Journal of Mathematics
publication date: 2006-01-24T00:00:00Z
review text: This paper is a part of the author's study about some aspects of Feynman's operational calculus. In the present work, the time-dependent stability is analysed. Here, stability properties using functions other than the exponential function are investigated. Also, differences between the results obtained here in the time-dependent setting and similar results for the time-independent setting are discussed. To do this, a brief presentation to the approach to Feynman's operational calculus is explained. Here, using noncommutative linear operators, some results for ``ordering'' are given. Also, the time-dependent disentangling map is defined. For the stability of the time-dependent operational calculus, first the stability with respect to the measures, then the stability with respect to operator-valued functions are treated.
reviewed by: Ilie Valuşescu
Mathematics Subject Classification ID: 47A60
Mathematics Subject Classification ID: 46J15
Mathematics Subject Classification ID: 47A56
Mathematics Subject Classification ID: 60B10
zbMATH DE Number: 5001010
zbMATH Keywords: functional calculus
zbMATH Keywords: Banach algebras
zbMATH Keywords: disentangling
zbMATH Keywords: operational calculus
zbMATH Keywords: stability
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181069689
OpenAlex ID: W1999673064
cites work: Q4269108
cites work: Feynman's operational calculus and evolution equations
cites work: Q4148368
cites work: Q4039882
cites work: An Operator Calculus Having Applications in Quantum Electrodynamics
cites work: Q4064235
cites work: Feynman's operational calculi for noncommuting operators: definitions and elementary properties
cites work: Feynman's operational calculus for families of noncommuting operators: tensor products, ordered supports, and the disentangling of an exponential factor
cites work: FEYNMAN'S OPERATIONAL CALCULI FOR NONCOMMUTING OPERATORS: SPECTRAL THEORY
cites work: Feynman's operational calculi for time dependent noncommuting operators
cites work: Generalized Dyson series, generalized Feynman diagrams, the Feynman integral and Feynman’s operational calculus
cites work: Q4954180
cites work: A stability theorem for Feynman's operational calculus
cites work: Q4359479
cites work: L-Nonformation, L-Ancillarity, and L-Sufficiency
cites work: Stability properties of Feynman's operational calculus for exponential functions of noncommuting operators
cites work: Effects of absolute continuity in Feynman’s operational calculus
DOI: 10.1216/RMJM/1181069689
Recommended article: Towards a comprehensive stability theory for Feynman's operational calculus: the time-dependent setting
Recommended article: Towards a comprehensive stability theory for Feynman's operational calculus: the time independent setting
Recommended article: A stability theorem for Feynman's operational calculus
Recommended article: Stability properties for Feynman's operational calculus in the combined continuous/discrete setting
Recommended article: Stability theorem for the Feynman integral via time continuation
Recommended article: Feynman's operational calculi for time dependent noncommuting operators
Recommended article: Stability properties of Feynman's operational calculus for exponential functions of noncommuting operators
Recommended article: Q3509357
Recommended article: Stability of Feynman-Kac formulae with path-dependent potentials
Recommended article: Q4727065
description: scientific article; zbMATH DE number 5001010