### Abstract

We establish a comprehensive stability theory for Feynman’s operational calculus (informally, the forming of functions of several noncommuting operators) in the time-dependent setting. Indeed, the main theorem, Theorem 2, contains many of the current stability theorems for the operational calculus and allows the stability theory to be significantly extended. The assumptions needed for the main theorem, Theorem 2, are rather mild and fit in nicely with the current abstract theory of the operational calculus in the time-dependent setting. Moreover, Theorem 2 allows the use of arbitrary time-ordering measures, as long as the discrete parts of these measures are finitely supported.

Original language | English (US) |
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Pages (from-to) | 1-31 |

Number of pages | 31 |

Journal | Acta Applicandae Mathematicae |

DOIs | |

State | Accepted/In press - Jun 16 2017 |

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### All Science Journal Classification (ASJC) codes

- Applied Mathematics

### Cite this

**Towards a Comprehensive Stability Theory for Feynman’s Operational Calculus : The Time-Dependent Setting.** / Nielsen, Lance.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Towards a Comprehensive Stability Theory for Feynman’s Operational Calculus

T2 - The Time-Dependent Setting

AU - Nielsen, Lance

PY - 2017/6/16

Y1 - 2017/6/16

N2 - We establish a comprehensive stability theory for Feynman’s operational calculus (informally, the forming of functions of several noncommuting operators) in the time-dependent setting. Indeed, the main theorem, Theorem 2, contains many of the current stability theorems for the operational calculus and allows the stability theory to be significantly extended. The assumptions needed for the main theorem, Theorem 2, are rather mild and fit in nicely with the current abstract theory of the operational calculus in the time-dependent setting. Moreover, Theorem 2 allows the use of arbitrary time-ordering measures, as long as the discrete parts of these measures are finitely supported.

AB - We establish a comprehensive stability theory for Feynman’s operational calculus (informally, the forming of functions of several noncommuting operators) in the time-dependent setting. Indeed, the main theorem, Theorem 2, contains many of the current stability theorems for the operational calculus and allows the stability theory to be significantly extended. The assumptions needed for the main theorem, Theorem 2, are rather mild and fit in nicely with the current abstract theory of the operational calculus in the time-dependent setting. Moreover, Theorem 2 allows the use of arbitrary time-ordering measures, as long as the discrete parts of these measures are finitely supported.

UR - http://www.scopus.com/inward/record.url?scp=85020499547&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85020499547&partnerID=8YFLogxK

U2 - 10.1007/s10440-017-0109-2

DO - 10.1007/s10440-017-0109-2

M3 - Article

SP - 1

EP - 31

JO - Acta Applicandae Mathematicae

JF - Acta Applicandae Mathematicae

SN - 0167-8019

ER -