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  Far East Journal of Mathematical Sciences (FJMS)  
 ISSN: 0972-0871
 
 
 

     Far East Journal of Mathematical Sciences (FJMS)
    Volume 24, Issue 3, Pages 385 - 396 (March 2007)


RELATIONSHIPS AMONG CONDITIONAL TRANSFORMS, CONDITIONAL CONVOLUTIONS AND FIRST VARIATIONS FOR SOME CONDITIONING FUNCTIONS

Bong Jin Kim (Korea)

Received September 19, 2006

References:



[1] R. H. Cameron and W. T. Martin, Fourier-Wiener transforms of analytic functionals, Duke Math. J. 12 (1945), 489-507.

[2] R. H. Cameron and D. A. Storvick, An analytic Fourier-Feynman transform, Michigan Math. J. 23 (1976), 1-30.

[3] R. H. Cameron and D. A. Storvick, Feynman integral of variations of functionals, Gaussian Random Fields (Nagoya, 1990), pp. 144-157, Ser. Probab. Statist., 1, World Sci. Publ., River Edge, NJ, 1991.

[4] K. S. Chang, B. S. Kim and I. Yoo, Integral transform and convolution of analytic functionals on abstract Wiener spaces, Numer. Funct. Anal. Optim. 21 (2000), 97-105.

[5] D. M. Chung and D. Skoug, Conditional analytic Feynman integrals and a related Schrödinger integral equation, SIAM J. Math. Anal. 20 (1989), 950-965.

[6] B. J. Kim, Conditional integral transforms, conditional convolution products and first variations for some conditioning functions, Far East J. Math. Sci. (FJMS) 19(3) (2005), 245 - 258.

[7] B. J. Kim, B. S. Kim and D. Skoug, Integral transforms, convolution products and first variations, Int. J. Math. Math. Sci. 11 (2004), 579-598.

[8] B. S. Kim and D. Skoug, Integral transforms of functionals in Rocky Mountain J. Math. 33 (2003), 1379 - 1393.

[9] Y. J. Lee, Integral transforms of analytic functions on abstract Wiener spaces, J. Funct. Anal. 47 (1982), 153-164.

[10] C. Park and D. Skoug, Conditional Fourier-Feynman transforms and conditional convolution products, J. Korean Math. Soc. 38 (2001), 61-76.

[11] C. Park and D. Skoug, A simple formula for conditional Wiener integrals with applications, Pacific J. Math. 135 (1988), 381-394.

[12] J. Yeh, Inversion of conditional Wiener integrals, Pacific J. Math. 59 (1975), 623-638.

Keywords and phrases: conditional Wiener integral, conditional integral transform, conditional convolution product, first variation.

 


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