### 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 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 operator-valued distributions of compact support in a ball of a certain radius centered at 0 ∈ 2 ℝ^{n}. In this way, we can extend the operational calculi to the Schwartz space.

Original language | English |
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Pages (from-to) | 377-398 |

Number of pages | 22 |

Journal | New York Journal of Mathematics |

Volume | 20 |

State | Published - 2014 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

**A distributional approach to Feynman's operational calculus.** / Nielsen, Lance.

Research output: Contribution to journal › Article

*New York Journal of Mathematics*, vol. 20, pp. 377-398.

}

TY - JOUR

T1 - A distributional approach to Feynman's operational calculus

AU - Nielsen, Lance

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84898432140&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84898432140&partnerID=8YFLogxK

M3 - Article

VL - 20

SP - 377

EP - 398

JO - New York Journal of Mathematics

JF - New York Journal of Mathematics

SN - 1076-9803

ER -