A distributional approach to Feynman's operational calculus

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Abstract

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 ∈ 2 ℝn. In this way, we can extend the operational calculi to the Schwartz space.

Original languageEnglish (US)
Pages (from-to)377-398
Number of pages22
JournalNew York Journal of Mathematics
Volume20
StatePublished - Jan 1 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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