• 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.

• 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.

• Journal of the Korean Mathematical Society
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• v.40 no.1
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• pp.73-86
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• 2003

In this paper, we define a generalized sequential operator-valued function space integral by using a generalized Wiener measure. It is an extention of the sequential operator-valued function space integral introduced by Cameron and Storvick. We prove the existence of this integral for functionals which involve some product Borel 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.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.293-303
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• 1997

The existence theorem for the operator valued function space integral has been studied, when the wave function was in $L_1(R)$ class and the potential energy function was represented as a double integra [4]. Johnson and Lapidus established the existence theorem for the operator valued function space integral, when the wave function was in $L_2(R)$ class and the potential energy function was represented as an integral involving a Borel measure [9]. In this paper, we establish the existence theorem for the operator valued function we establish the existence theorem for the operator valued function space integral as an operator from $L_1(R)$ to $L_\infty(R)$ for certain potential energy functions which involve double integrals with some Borel measures.

• 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 $C^t to C$.

• 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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.579-584
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• 1998

In this work, we present a method to deal with the interval valued decision making systems. First, we propose a new type of equality measure based on the Ordered Weighted Averaging (OWA) operator. The proposed equality measure has a structure to render the extreme values of the measure by choosing a suitable weighting vector of the OWA operator. From this property, we derive a bidirectional fuzzy inference network which can be applied for the decisionmaking systems requiring the inverval valued decisions.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.285-295
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• 2013

In this note we present sufficient conditions for the existence of Radon-Nikodym derivatives (RND) of operator valued measures with respect to scalar measures. The RND is characterized by the Bochner integral in the strong operator topology of a strongly measurable operator valued function with respect to a nonnegative finite measure. Using this result we also obtain a characterization of compact sets in the space of operator valued measures. An extension of this result is also given using the theory of Pettis integral. These results have interesting applications in the study of evolution equations on Banach spaces driven by operator valued measures as structural controls.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.331-336
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• 1994

Let $P_{0}$ be a $\delta$-ring (a ring closed with respect to the forming of countable intersections) of subsets of a nonempty set $\Omega$. Let X and Y be Banach spaces and L(X, Y) the Banach space of all bounded linear operators from X to Y. A set function m : $P_{0}$ longrightarrow L(X, Y) is called an operator valued measure countably additive in the strong operator topology if for every x $\epsilon$ X the set function E longrightarrow m(E)x is a countably additive vector measure. From now on, m will denote an operator valued measure countably additive in the strong operator topology.(omitted)