# A NOTE ON AXIOMATIC FEYNMAN OPERATIONAL CALCULUS

• Park, Yeon-Hee (Department of Mathematics Education, Institute of Pure and Applied Mathematics, Chonbuk National University)
• Accepted : 2012.05.29
• Published : 2012.06.25

#### Abstract

In this note we prove the space (A, ${\parallel}.{\parallel}$) is a Banach space and ${\parallel}ab{\parallel}{\leq}{\parallel}a{\parallel}{\parallel}b{\parallel}$ for $a,b{\in}A$ where $A:=\{a:=(a_t)_{t{\in}G}:{\sum}_{t{\in}G}{\parallel}a_t{\parallel}_t<{\infty}\}$, $G=\mathbb{N}^*$. Also we show some property in (A, ${\parallel}.{\parallel}$).

#### References

1. Johnson, G.W. and Lapidus, M.L., Generalized Dyson series, generalized Feynman diagram, the Feynman integral and Feynman's operational calculus, Memoirs Amer. Math. Soc. 62, No. 351,1986, 1-78.
2. Johnson, G.W. and Lapidus, M.L., Noncommutativ operations on Wiener functionals and Feynman's operational calculus, J. Functional Anal. 81, 1988, 74-99. https://doi.org/10.1016/0022-1236(88)90113-9
3. Lapidus, M.L., Quentification, calcul operationnel de Feynman axiomatique et integrale fonctionnelle generalisee, C.R. Acad.Sci. Paris, t. 308, Serie I, p. 133- 138, 1989.
4. Johnson, G.W. and Lapidus, M.L., The Feynman Integral and Feynman's operational calculus, OXFORD university Press, 2000.