 

Lance Nielsen
A distributional approach to Feynman's operational calculus view print


Published: 
April 12, 2014

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


Abstract
In this paper we will construct an operatorvalued distribution that
will extend Feynman's operational calculus in the setting of Jefferies
and Johnson, 20012003, and JohnsonLapidusNielsen, 2014,
from the disentangling
of holomorphic functions of several variables to the disentangling
of Schwartz functions on R^{n}. 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 operatorvalued distributions of compact support
in a ball of a certain radius centered at 0∈R^{n}. In
this way, we can extend the operational calculi to the Schwartz space.


Author information
Department of Mathematics, Creighton University, Omaha, NE 68178
lnielsen@creighton.edu

