New York Journal of Mathematics
Volume 20 (2014) 377-398


Lance Nielsen

A distributional approach to Feynman's operational calculus

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Published: April 12, 2014
Keywords: Feynman's operational calculus; disentangling; Schwartz space; generalized functions; distributions; Fourier transform
Subject: 46F10, 46F12, 47B48, 47B38

In this paper we will construct an operator-valued distribution that will extend Feynman's operational calculus in the setting of Jefferies and Johnson, 2001-2003, and Johnson-Lapidus-Nielsen, 2014, from the disentangling of holomorphic functions of several variables to the disentangling of Schwartz functions on Rn. It will be shown that the disentangled operator corresponding to a Schwartz function (i.e., the disentangling of a Schwartz function) can be realized as the limit of a sequence of operator-valued distributions of compact support in a ball of a certain radius centered at 0∈Rn. In this way, we can extend the operational calculi to the Schwartz space.

Author information

Department of Mathematics, Creighton University, Omaha, NE 68178