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 language||English (US)|
|Number of pages||22|
|Journal||New York Journal of Mathematics|
|State||Published - Jan 1 2014|
All Science Journal Classification (ASJC) codes