• Honam Mathematical Journal
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• v.40 no.3
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• pp.577-589
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• 2018

In this note we give some results of the disentangling algebras and disentangling maps and calculate functions on disentangling via measures.

• 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.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.193-226
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• 2001

We study Feynman's Operational Calculus for operator-valued functions of time and for measures which are not necessarily probability measures; we also permit the presence of certain unbounded operators. further, we relate the disentangling map defined within the solutions of evolution equations and, finally, remark on the application of stability results to the present paper.

• 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.

• The Bulletin of The Korean Astronomical Society
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• v.32 no.1
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• pp.91.2-91.2
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• 2007

• 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.

• 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.

• 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.

• 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.