Two approaches to the use of unbounded operators in feynman’s operational calculus

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Abstract

In this paper, we investigate two approaches to the use of unbounded operators in Feynman’s operational calculus. The first involves using a functional calculus for unbounded operators introduced by A. E. Taylor in the paper [34]. The second approach uses analytic families of closed unbounded operators as discussed in [19]. For each approach, we discuss the essential properties of the operational calculus as well as continuity (or stability) properties. Finally, for the approach using the Taylor calculus, we discussion a connection between Feynman’s operational calculus in this setting with the Modified Feynman Integral of M. L. Lapidus ([14, 20]).

Original languageEnglish (US)
Pages (from-to)378-445
Number of pages68
JournalNew York Journal of Mathematics
Volume26
StatePublished - Jan 1 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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