TY - JOUR

T1 - Feynman’s Operational Calculus with Arbitrary Measures

T2 - An Evolution Equation in the General Case and Examples

AU - Nielsen, Lance

N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

PY - 2022/6

Y1 - 2022/6

N2 - In this paper we present the abstract approach to Feynman’s operational calculus in the most general setting, in which the time-ordering measures are allowed to have arbitrarily supported discrete parts. Two approaches to the operational calculus are presented in detail and examples of each method are presented. In particular, for the second method we present an evolution equation satisfied by the operational calculus and examples (Feynman–Kac formulas with Lebesgue–Stieltjes measures) are considered. Furthermore, a basic stability (or continuity) result is presented.

AB - In this paper we present the abstract approach to Feynman’s operational calculus in the most general setting, in which the time-ordering measures are allowed to have arbitrarily supported discrete parts. Two approaches to the operational calculus are presented in detail and examples of each method are presented. In particular, for the second method we present an evolution equation satisfied by the operational calculus and examples (Feynman–Kac formulas with Lebesgue–Stieltjes measures) are considered. Furthermore, a basic stability (or continuity) result is presented.

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U2 - 10.1007/s00020-022-02694-4

DO - 10.1007/s00020-022-02694-4

M3 - Article

AN - SCOPUS:85128272505

SN - 0378-620X

VL - 94

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 2

M1 - 15

ER -