Feynman’s Operational Calculus with Arbitrary Measures: An Evolution Equation in the General Case and Examples

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Abstract

In this paper we present the abstract approach to Feynman’s operational calculus in the most general setting, in which the time-ordering measures are allowed to have arbitrarily supported discrete parts. Two approaches to the operational calculus are presented in detail and examples of each method are presented. In particular, for the second method we present an evolution equation satisfied by the operational calculus and examples (Feynman–Kac formulas with Lebesgue–Stieltjes measures) are considered. Furthermore, a basic stability (or continuity) result is presented.

Original languageEnglish (US)
Article number15
JournalIntegral Equations and Operator Theory
Volume94
Issue number2
DOIs
StatePublished - Jun 2022

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory

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