• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.569-579
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• 1997

We investigate the existence of the operator-valued Feynman integral when a Wiener functional is given by a Fourier transform of complex Borel measure.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.21-29
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• 2002

The existence of the operator-valued Feynman integral was established when a Wiener functional is given by a Fourier transform of complex Borel measures. In this paper, we investigate the stability of the Feynman integral with respect to the measures.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.959-968
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• 2000

The existence of the operator-valued Feynman integral was established when a Wiener functional is given by a Fourier transform of complex Borel measure [1]. In this paper, I investigate a stability of the Feynman integral with respect to the potentials.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.903-924
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• 2016

In the present paper, using a simple formula for the conditional expectations given a generalized conditioning function over an analogue of vector-valued Wiener space, we prove that the analytic operator-valued Feynman integrals of certain classes of functions over the space can be expressed by the conditional analytic Feynman integrals of the functions. We then provide the conditional analytic Feynman integrals of several functions which are the kernels of the analytic operator-valued Feynman integrals.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.349-363
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• 2001

The analytic in mass operator-valued Feynman integral is related to integration with respect to unbounded set functions formed from the semigroup obtained by analytic continuation of the heat semigroup and the spectral measure of multiplication by characteristics functions.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.465-475
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• 1996

Fix t > 0. Denote by $C^t$ the space of $R$-valued continuous functions x on [0,t]. Let $C_0^t$ be the Wiener space - $C_0^t = {x \in C^t : x(0) = 0}$ - equipped with Wiener measure m. Let F be a function from $C^t to C$.

• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.999-1018
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• 1998

In this paper, we prove stability theorems for the operator-valued Feynman integral of certain functionals involving some Borel measures on (0, t) as a bounded linear operator from L$_1$(R) to $C_{0}$(R).

• Journal of the Chungcheong Mathematical Society
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• v.8 no.1
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• pp.119-130
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• 1995

I study the extension of the definition of the analytic operator-valued Feynman integral to potentials given by a class of signed measures described in terms of additive functionals associated with regular Dirichlet forms.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.37-48
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• 2010

In this paper we use a generalized Brownian motion process to defined an analytic operator-valued generalized Feynman integral. We then obtain explicit formulas for the analytic operatorvalued generalized Feynman integrals for functionals of the form $$F(x)=f\({\int}^T_0{\alpha}_1(t)dx(t),{\cdots},{\int}_0^T{\alpha}_n(t)dx(t)\)$$, where x is a continuous function on [0, T] and {${\alpha}_1,{\cdots},{\alpha}_n$} is an orthonormal set of functions from ($L^2_{a,b}[0,T]$, ${\parallel}{\cdot}{\parallel}_{a,b}$).

• Journal for History of Mathematics
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• v.14 no.2
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• pp.21-28
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• 2001

In this paper we introduce the Feynman integral which is one of the function space integrals. There are so many approaches to the Feynman integral. Here we treat tile analytic Feynman integral and the operator-valued Feynman integral.