Towards a Comprehensive Stability Theory for Feynman’s Operational Calculus

The Time-Dependent Setting

Research output: Contribution to journalArticle

Abstract

We establish a comprehensive stability theory for Feynman’s operational calculus (informally, the forming of functions of several noncommuting operators) in the time-dependent setting. Indeed, the main theorem, Theorem 2, contains many of the current stability theorems for the operational calculus and allows the stability theory to be significantly extended. The assumptions needed for the main theorem, Theorem 2, are rather mild and fit in nicely with the current abstract theory of the operational calculus in the time-dependent setting. Moreover, Theorem 2 allows the use of arbitrary time-ordering measures, as long as the discrete parts of these measures are finitely supported.

Original languageEnglish (US)
Pages (from-to)1-31
Number of pages31
JournalActa Applicandae Mathematicae
DOIs
StateAccepted/In press - Jun 16 2017

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Operational Calculus
Stability Theory
Theorem
Mathematical operators
Stability Theorem
Arbitrary
Operator

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Cite this

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