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Parts formulas involving conditional Feynman integrals

Published online by Cambridge University Press:  17 April 2009

Seung Jun Chang  and
David Skoug
Seung Jun Chang
Affiliation:
Department of Mathematics, Dankook University, Cheonan 330–714, Korea, e-mail: sejchang@dankook.ac.kr
David Skoug
Affiliation:
Department of Mathematics and Statistics, University of Nebraska-Lincoln, Lincoln, NE 68588–0323, United States of America, e-mail: dskoug@math.unl.edu
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Abstract

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In this paper we first obtain a basic formula for the conditional analytic Feynman integral of the first variation of a functional on Wiener space. We then apply this basic result to obtain several integration by parts formulas for conditional analytic Feynman integrals and conditional Fourier-Feynman transforms.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 65 , Issue 3 , June 2002 , pp. 353 - 369
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Brue, M.D., A functional transform for Feynman integrals similar to the Fourier transform, Ph.D. Thesis (University of Minnesota, Minneapolis, 1972).Google Scholar
[2]Cameron, R.H., ‘The first variation of an indefinite Wiener integral’, Proc. Amer. Math. Soc. 2 (1951), 914–924.CrossRefGoogle Scholar
[3]Cameron, R.H. and Storvick, D.A., ‘A translation theorem for analytic Feynman integrals’, Trans. Amer. Math. Soc. 125 (1966), 1–6.CrossRefGoogle Scholar
[4]Cameron, R.H. and Storvick, D.A., ‘An L 2 analytic Fourier-Feynman transform’, Michigan Math. J. 23 (1976), 1–30.CrossRefGoogle Scholar
[5]Cameron, R.H. and Storvick, D.A., ‘Some Banach algebras of analytic Feynman integrable functionals,’, in Analytic functions (Kozubnik, 1979), Lecture Note in Math. 798 (Springer-Verlag, Berlin, New York, 1980), pp. 18–67.CrossRefGoogle Scholar
[6]Cameron, R.H. and Storvick, D.A., ‘Feynman integral of variations of functions, in Gaussian random fields’, Ser. Probab. Statist 1 (1991), 144–157.Google Scholar
[7]Chang, K.S., ‘Scale-invariant measurability in Yeh-Wiener space’, J. Korean Math. Soc. 19 (1982), 61–67.Google Scholar
[8]Chang, S.J. and Chung, D.M., ‘A class of conditional Wiener integrals’, J. Korean Math. Soc. 30 (1993), 161–172.Google Scholar
[9]Chang, S.J., Park, C. and Skoug, D., ‘Translation theorems for Fourier-Feynman transforms and conditional Fourier-Feynman transforms’, Rocky Mountain J. Math. 30 (2000), 477–496.CrossRefGoogle Scholar
[10]Chang, S.J. and Skoug, D., ‘The effect of drift on the Fourier-Feynman transform, the convolution product and the first variation’, Int. J. Appl. Math. 2 (2000), 505–527.Google Scholar
[11]Chung, D.M. and Skoug, D.L., ‘Conditional analytic Feynman integrals and a related Schrödinger integral equation’, SIAM J. Math. Anal. 20 (1989), 950–965.CrossRefGoogle Scholar
[12]Johnson, G.W. and Skoug, D.L., ‘An Lp analytic Fourier-Feynman transform’, Michigan Math. J. 26 (1979), 103–127.CrossRefGoogle Scholar
[13]Johnson, G.W. and Skoug, D.L., ‘Scale-invariant measurability in Wiener space’, Pacific J. Math. 83 (1979), 157–176.CrossRefGoogle Scholar
[14]Kim, J., Ko, J., Park, C. and Skoug, D., ‘Relationships among transforms, convolutions and first variations’, Internat. J. Math. Sci. 22 (1999), 191–204.Google Scholar
[15]Park, C. and Skoug, D., ‘A simple formula for conditional Wiener integrals with applications’, Pacific J. Math. 135 (1988), 381–394.CrossRefGoogle Scholar
[16]Park, C. and Skoug, D., ‘A Kac-Feynman integral equation for conditional Wiener integrals’, J. Integral Equations Appl. 3 (1991), 411–427.CrossRefGoogle Scholar
[17]Park, C. and Skoug, D., ‘Conditional Fourier-Feynman transforms and conditional convolution products’, J. Korean Math. Soc. 38 (2001), 61–76.Google Scholar
[18]Park, C. and Skoug, D., ‘Integration by parts formulas involving analytic Feynman integrals’, Panamer. Math. J. 8 (1998), 1–11.Google Scholar
[19]Park, C., Skoug, D. and Storvick, D., ‘Relationships among the first variation, the convolution product, and the Fourier-Feynman transforms’, Rocky Mountain J. Math. 28 (1998), 1447–1468.Google Scholar
[20]Yeh, J., ‘Inversion of conditional Wiener integrals’, Pacific J. Math. 59 (1975), 623–638.CrossRefGoogle Scholar