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New York Journal of Mathematics
Volume 26 (2020), 378-445

  

Lance Nielsen

Two approaches to the use of unbounded operators in Feynman's operational calculus

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Published: April 22, 2020.
Keywords: operational calculus, disentangling, unbounded operators, time-ordering, Taylor calculus, analytic families of operators, stability theory, modified Feynman integral.
Subject: 44A99, 47A10, 47A13, 47A60, 47B15, 47B25, 47B48, 46G10.

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]).

Acknowledgements

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Author information

Lance Nielsen:
Department of Mathematics
Creighton University
Omaha, NE 68178, USA

lnielsen@creighton.edu