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Algebres nucleaires de fonctions entières et equations aux derivées partielles stochastiques

Published online by Cambridge University Press:  22 January 2016

H. Ouerdiane
H. Ouerdiane*
Affiliation:
Departement de Mathematques, Faculte des Sciences de Tunis, Campus Universitaire, 1060-Tunis-Tunisie, [email protected]
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En analyse du bruit blanc (W.N.A) on utilise usuellement le triplet de Gelfand (S(R) ⊂ L2(R, dt) ⊂ S′(R), μ) où S′(R) est l’espace de L. Schwartz des distributions tempérées et μ la mesure Gaussienne donnée par sa fonction caractéristique:

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Type
Research Article
Information
Nagoya Mathematical Journal , Volume 151 , September 1998 , pp. 107 - 127
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1998

References

Bibliographie

[1] Benth, F., Deck, T., Potthoff, J. and Streit, L., Evolution equations with multiplicative noise, Preprint (1995).Google Scholar
[2] Chow, P. L., Generalized solution of some parabolic equations with a random drift, J. App. Math. Optimization, 20 (1989), 81–96.Google Scholar
[3] Chung, D. M. and Ji, U. C., Cauchy problems for a partial differential equation in white noise analysis, J. Korean math. Soc, 33 (1996), 309–318.Google Scholar
[4] Dwyer, T., Partial differential equations in Fischer-Fock spaces, Bull. A. M. S., 5 (1971), 725–730.CrossRefGoogle Scholar
[5] Fernique, X., Processus linéaires-processus généralisées, Annales de l’institut de Fourier, Tome XVII. 1, 1–92.Google Scholar
[6] Gross, L., Potential theory on Hilbert space, J. Funct. Anal., 1 (1967), 123–181.CrossRefGoogle Scholar
[7] Grothendieck, A., Produits tensoriels topologiques et espaces nucléaires, Memoirs of the A. M. S., 16 (1955), 1–140.Google Scholar
[8] Hida, T., Brownian Motion, Springer, Berlin, Heidelberg, New-York, 1980.CrossRefGoogle Scholar
[9] Hida, T., Kuo, H. H., Potthoff, J. and Streit, L., White noise an infinite dimensional calculus, Maths, and its applications (1993), Kluwer Academic Publishers.Google Scholar
[10] Holden, H., Lindstrom, T., Oksendal, B., Uboe, J. and Zhang, T. S., The Burgers Equation with a noisy force and the stochastic Heat equation, Comm. P. D. E., 19 (1994).CrossRefGoogle Scholar
[11] Holden, H., Lindstrom, T., Oksendal, B., Uboe, J. and Zhang, T. S., The stochastic wick-type Burgers equation, London Math. Soc, 216 (1995), 141–161.Google Scholar
[12] Kondrat’ev, Y. G., Nuclear spaces of entire functions in problems of infinite dimensional analysis, Soviet. Math. Dokl., 22 (1980), 588–592.Google Scholar
[13] Kondrat’ev, Y. G., Streit, L. and Westerkamp, W., A note on positive distributions in Gaussian analysis, Ukrain. Math., 47 (1995), 649–658.Google Scholar
[14] Kree, P., and Raczka, R., Kernels and symbols of operators in quantum field theory, Ann. Ins. H. Poincaré, 28 (1978), 41–73.Google Scholar
[15] Kree, P., Distributions en dimension quelconque et intégrales stochastiques, Conf. Silivri (1986), L. N. M. No. 1316 (1988), pp. 170–233.Google Scholar
[16] Kree, P., Distributions, Sobolev spaces on Gaussian spaces and Ito’s calculus, Stochastic Processes and their applications (S. Albeverio and all, eds.), Kluwer Academic Pub. (1990), pp. 203–225.CrossRefGoogle Scholar
[17] Kubo, I. and Takenaka, S., Calculus on Gaussian white noise I, Proc. Japan Acad., 56 (1980), 376–380.Google Scholar
[18] Kuo, H. H., Potthoff, J. and Streit, L., A characterization of white noise test functional, Nagoya Math. J., 121 (1991), 185–194.CrossRefGoogle Scholar
[19] Kuo, H.-H., White Noise Distribution Theory, CRC Press, 1996.Google Scholar
[20] Meyer, P. A. and Yan, J. A., Les fonctions caractéristiques des distributions sur l’espace de Wiener, Séminaire de Probabilités XXV, L. N. M. No. 1485, Springer-Verlag, 1991, pp. 61–78.Google Scholar
[21] Ouerdiane, H., Dualité et opérateurs de convolution dans certains espaces de fonctions entières nucléaires à croissance exponentielles, Abhandlungen aus der math. Séminar Univ. Hamburg. Germany., 54 (1983), 276–283.CrossRefGoogle Scholar
[22] Ouerdiane, H., Application des méthodes d’holomorphie et de distributions en dimension quelconque à l’analyse sur les espaces gaussiens, BiBos No. 491 (1991).Google Scholar
[23] Ouerdiane, H., Extension de deux théorèmes de type Kondrat’ev-Yokoi, BiBoS No. 572 (1993).Google Scholar
[24] Ouerdiane, H., Fonctionnelles analytiques avec condition de croissance et application à l’analyse gaussienne, Japanese Journal of Math., 20 No. 1 (1994), 187–198.Google Scholar
[25] Ouerdiane, H., Noyaux et Symboles d’opérateurs sur des fonctionnelles analytiques-Gaussiennes, BiBoS No. 634, Japanse Journal of Math., 21 No. 1 (1995), 223–234.Google Scholar
[26] Obata, N., An analytic characterization of symbols of operators on white noise functionals, J. Math. Soc. Japan, 45 No. 3 (1993), 421–445.CrossRefGoogle Scholar
[27] Obata, N., White noise calculus and Fock space, L. N. M. No. 1577, Springer-Verlag, 1994.Google Scholar
[28] Piech, M. A., A fundamental solution of the parabolic equation on Hilbert space, J. Funct. Anal., 3 (1969), 85–114.CrossRefGoogle Scholar
[29] Piech, M. A., Parabolic equations associated with the number operator, Trans. Amer. Math. Soc, 194 (1974), 213–222.CrossRefGoogle Scholar
[30] Potthoff, J., On positive generalized functionals, J. Funct. Anal., 74 (1987), 81–95.CrossRefGoogle Scholar
[31] Potthoff, J., White noise approach to parabolic stochastic partial differential equations, Stochastic analysis and Applications in Physics NATO-ASI. Séries (In A. I. Cardoso et al, eds.), 499, Kluwer Academic Publishers (1994).Google Scholar
[32] Streit, L., An introduction to white Noise Analysis, BiBoS No. 641, Preprint (1994).Google Scholar
[33] Schwartz, L., Distributions à valeurs vectorielles, Annales de l’Institut Fourier, Tome 7 (1957) et Tome 8 (1959).Google Scholar
[34] Yokoi, I., Positive generalized white noise functionals, Hiroshima Math. J., 20 (1990), 137–157.CrossRefGoogle Scholar