References
- Brue M. D., A functional transform for Feynman integrals similar to the Fourier transform, Thesis, Univ. of Minnesota, Minneapolis, 1972.
- Cameron R. H., Storvick D. A., Some Banach algebras of analytic Feynman integrable functionals, Lecture Notes in Mathematics 798, Springer, Berlin-New York, 1980.
- Chang K. S., Cho D. H., Kim B. S., Song T. S., Yoo I., Conditional Fourier-Feynman transform and convolution product over Wiener paths in abstract Wiener space, Integral Transforms Spec. Funct. 14(3) (2003), 217-235. https://doi.org/10.1080/1065246031000081652
- Chang S. J., Skoug D., The effect of drift on conditional Fourier-Feynman transforms and conditional convolution products, Int. J. Appl. Math. 2(4) (2000), 505-527.
- Cho D. H., A time-dependent conditional Fourier-Feynman transform and convolution product on an analogue of Wiener space, Houston J. Math. 2012, submitted.
- Cho D. H., Conditional integral transforms and conditional convolution products on a function space, Integral Transforms Spec. Funct. 23(6) (2012), 405-420. https://doi.org/10.1080/10652469.2011.596482
- Cho D. H., A simple formula for an analogue of conditional Wiener integrals and its applications II, Czechoslovak Math. J. 59(2) (2009), 431-452. https://doi.org/10.1007/s10587-009-0030-6
-
Cho D. H., Conditional Fourier-Feynman transform and convolution product over Wiener paths in abstract Wiener space: an
$L_p$ theory, J. Korean Math. Soc. 41(2) (2004), 265-294. https://doi.org/10.4134/JKMS.2004.41.2.265 - Cho D. H., Kim B. J., Yoo I., Analogues of conditional Wiener integrals and their change of scale transformations on a function space, J. Math. Anal. Appl. 359 (2009), 421-438. https://doi.org/10.1016/j.jmaa.2009.05.023
- Folland G. B., Real analysis, John Wiley & Sons, New York-Chichester-Brisbane, 1984.
- Huffman T., Park C., Skoug D., Analytic Fourier-Feynman transforms and convolution, Trans. Amer. Math. Soc. 347(2) (1995), 661-673. https://doi.org/10.1090/S0002-9947-1995-1242088-7
- Im M. K., Ryu K. S., An analogue of Wiener measure and its applications, J. Korean Math. Soc. 39(5) (2002), 801-819. https://doi.org/10.4134/JKMS.2002.39.5.801
-
Johnson G. W., Skoug D. L., The Cameron-Storvick function space integral: an L(
$L_p,\;L_p'$ )-theory, Nagoya Math. J. 60 (1976), 93-137. https://doi.org/10.1017/S0027763000017189 - Kim M. J., Conditional Fourier-Feynman transform and convolution product on a function space, Int. J. Math. Anal. 3(10) (2009), 457-471.
- Laha R. G., Rohatgi V. K., Probability theory, John Wiley & Sons, New York-Chichester-Brisbane, 1979.
- Ryu K. S., Im M. K., A measure-valued analogue of Wiener measure and the measure-valued Feynman-Kac formula, Trans. Amer. Math. Soc. 354(12) (2002), 4921-4951. https://doi.org/10.1090/S0002-9947-02-03077-5
- Ryu K. S., Im M. K., Choi K. S., Survey of the theories for analogue of Wiener measure space, Interdiscip. Inform. Sci. 15(3) (2009), 319-337.
- Stein E. M., Weiss G., Introduction to Fourier analysis on Euclidean spaces, Princeton Univ. Press, Princeton, 1971.
- Yeh J., Stochastic processes and the Wiener integral, Marcel Dekker, New York, 1973.
Cited by
- CONDITIONAL FOURIER-FEYNMAN TRANSFORMS AND CONVOLUTIONS OF UNBOUNDED FUNCTIONS ON A GENERALIZED WIENER SPACE vol.50, pp.5, 2013, https://doi.org/10.4134/JKMS.2013.50.5.1105