• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.485-493
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• 2005

A variety of Feynman's operational calculus for noncommuting operators was studied [2,3,4,5,6]. And a stability in the measures for Feynman's operational calculus was studied [9]. In this paper, we investigate a stability of the Feynman's operational calculus with respect to the operators.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.337-348
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• 1995

In 1987, Johnson and Lapidus introduced the noncommutative operations * and + on Wiener functionals and gave a precise and rigorous interpretation of certain aspects of Feynman's operational calculus for noncommuting operators. They established the operational calculus for certain functionals which involve Legesgue measure. In this paper we establish the operational calculus for the functionals applied to multiple integrals which involve some Borel measures.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.479-487
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• 2007

A variety of Feynman's operational calculus for noncommuting operators was studied [3,4,5,6,7,10]. And a stability in the continuous measures for Feynman's operational calculus was studied [9]. In this paper, we investigate a stability of the Feynman's operational calculus in the setting where the time-ordering measures are allowed to have both continuous and discrete parts.

• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.721-730
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• 2004

Feynman's operational calculus for noncommuting operators was studied via measures on the time interval. We investigate that if a sequence of p-tuples of measures converges to another p-tuple of measures, then the corresponding sequence of operational calculi in the time dependent setting converges to the operational calculus determined by the limiting p-tuple of measures.

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.703-715
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• 2006

Recently, we proved the existence theorem of measure-valued Feynman-Kac formula and showed that it satisfied Volterra's integral equation. In this paper, we establish the operational calculus for a measure-valued Dyson series and give some examples related to the measure-valued Dyson series.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.531-541
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• 2012

Feynman's operational calculus for noncommuting operators was studied by means of measures on the time inteval. And various stability theorems for Feynman's operational calculus were investigated. In this paper we see the time-dependent stability properties when the operator-valued functions take their values in a separable Hilbert space.

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.429-438
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• 2015

In this paper, we discuss how the operational calculus can be exploited to the theory of mixed generating functions. We use operational methods associated with multi-variable Hermite polynomials, Laguerre polynomials and Bessels functions to drive identities useful in electromagnetism, fluid mechanics etc. Certain special cases giving bilateral generating relations related to these special functions are also discussed.

• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.573-587
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• 2004

Disentangling is the essential operation of Feynman's operational calculus for noncommuting operators. Thus formulas which simplify this operation are central to the subject. In a recent paper the procedure for 'extracting a linear factor' has been established in the setting of Feynman's operational calculus for time independent operators $A_1, ... , A_n$ and associated probability measures ${\mu}_1,..., {\mu}_n$. While the setting just described is natural in many circumstances, it is not natural for evolution problems. There the measures should not be restricted to probability measures and it is worthwhile to allow the operators to depend on time. The main purpose for this paper is to extend the procedure for extracting a linear factor to this latter setting. We should mention that Feynman's primary motivation for developing an operational calculus for noncommuting operators came from a desire to describe the evolution of certain quantum systems.m systems.

• Communications of the Korean Mathematical Society
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• v.23 no.1
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• pp.67-80
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• 2008

Feynman's operational calculus for noncommuting operators was studied via measures on the time interval. We investigate some properties of Feynman's operational calculi which include a variety of blends of discrete and continuous measures in the time dependent setting.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.931-938
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• 2010

The disentangling map from the commutative algebra to the noncommutative algebra of operators is the essential operation of Feynman's operational calculus for noncommuting operators. Thus formulas which simplify this operation are meaningful to the subject. In a recent paper the procedure for "methods for iterative disentangling" has been established in the setting of Feynman's operational calculus for time independent operators $A_1$, $\cdots$, $A_n$ and associated probability measures${\mu}_1$, $\cdots$, ${\mu}_n$. The main purpose for this paper is to extend the procedure for methods for iterative disentangling to time dependent operators.