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(1999 / vol.2 / no.1)
Stability of Analytic Operator-Valued Function Space Integrals
Kun Soo Chang
Pages. 181-188     



Since the Feynman integral was introduced by Feynman in 1948,
there has been considerable progress on stability of Feynman integrals in recent
years. The first stability theorem for the integral was introduced by Johnson
in 1984 as a bounded linear operator on $L_2(Bbb{R})$ and it was extended to the
case of $L_p(Bbb{R})$ with respect to measures, potentials and wave of functions. In
this paper, we will briefly review the previous results and introduce the recent
results on the stability of analytic operator-valued function space integrals.



1. Introduction
2. Stability theorems involving the Lebesgue measure
3. Stability theorems involving Borel mesures
4. Stability theorems : $mathcal{L}(L_1(Bbb{R}, C_0(Bbb{R}))$ theory



Feynman integral, operator-valued function space integral, stability theorem, potential, wave function, measure, bounded linear operator



28C20