On Fourier transform of generalized Brownian functionals. (English) Zbl 0491.60039


60G20 Generalized stochastic processes
60J65 Brownian motion
42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
46F25 Distributions on infinite-dimensional spaces
60G15 Gaussian processes
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
42C99 Nontrigonometric harmonic analysis


Zbl 0432.60002
Full Text: DOI


[1] Gel’fand, I. M.; Vilenkin, N. Ya, Generalized functions, (Applications of Harmonic Analysis, Vol. 4 (1964), Academic Press) · Zbl 0136.11201
[2] Hida, T., (Analysis of Brownian Functionals (1975), Carleton University: Carleton University Ottawa), Carleton Math. Lecture Notes, No. 13 · Zbl 1089.60522
[3] Hida, T., Generalized multiple Wiener integrals, (Proc. Japan Acad. Ser. A Math. Sci., 54 (1978)), 55-58 · Zbl 0389.60026
[4] Hida, T., (Brownian Motion, Application of Math., Vol. 11 (1980), Springer-Verlag: Springer-Verlag Heidelberg/Berlin/New York) · Zbl 0432.60002
[5] Hida, T., The role of exponential functions in the analysis of generalized Brownian functionals (1981), Preprint · Zbl 0495.60047
[6] Kubo, I.; Takenaka, S., Calculus on Gaussian white noise I, (Proc. Japan Acad. Ser. A Math. Sci., 56 (1980)), 376-380 · Zbl 0459.60068
[7] Kubo, I.; Takenaka, S., Calculus on Gaussian white noise II, (Proc. Japan Acad. Ser. A Math. Sci., 56 (1980)), 411-416 · Zbl 0475.60064
[8] Kuo, H.-H, Integration by parts for abstract Wiener measures, Duke Math. J., 41, 373-379 (1974) · Zbl 0312.28012
[9] Kuo, H.-H, Fourier-Wiener transform on Brownian functionals, (Lecture Notes in Math. No. 828 (1980), Springer-Verlag: Springer-Verlag Heidelberg/Berlin/New York), 146-161 · Zbl 0445.60064
[10] Streit, L.; Hida, T., Generalized Brownian functionals and Feynman integral (1981), Preprint · Zbl 0575.60039
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.