A distributional approach to Feynman%26apos;s operational calculus

作者：Nielsen Lance^*

来源：The New York Journal of Mathematics, 2014, 20: 377-398.

• Feynman%26apos
• s operational calculus
• disentangling
• Schwartz space
• generalized functions
• distributions
• Fourier transform

In this paper we will construct an operator-valued distribution that will extend Feynman%26apos;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 R-n. It will be shown that the disentangled operator corresponding to a Schwartz 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 is an element of R-n. In this way, we can extend the operational calculi to the Schwartz space.

• 出版日期2014