Hiroshima Mathematical Journal

Generalized functions in infinite-dimensional analysis

Yuri G. Kondratiev, Ludwig Streit, Werner Westerkamp, and Jia-an Yan

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Hiroshima Math. J., Volume 28, Number 2 (1998), 213-260.

First available in Project Euclid: 21 March 2008

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Primary: 46F25: Distributions on infinite-dimensional spaces [See also 58C35]
Secondary: 46E50: Spaces of differentiable or holomorphic functions on infinite- dimensional spaces [See also 46G20, 46G25, 47H60] 60H99: None of the above, but in this section


Kondratiev, Yuri G.; Streit, Ludwig; Westerkamp, Werner; Yan, Jia-an. Generalized functions in infinite-dimensional analysis. Hiroshima Math. J. 28 (1998), no. 2, 213--260. doi:10.32917/hmj/1206126760. https://projecteuclid.org/euclid.hmj/1206126760

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  • [1] S. Albeverio, Yu. G. Kondratiev, and L. Streit, How to generalize White Noise Analysis to Non-Gaussian Spaces. In: 'Dynamics of Complex and Irregular Systems', Eds.: Ph. Blanchard et al., World Scientific, 1993.
  • [2] S. Albeverio, Y. Daletzky, Yu. G. Kondratiev, and L. Streit, Non-Gaussian infinite dimensional analysis, J. Funct. Anal. 138, (1996), 311-350.
  • [3] F. Benth and L. Streit, The Burgers Equation with a Non-Gaussian Random Force. Madeira preprint 17/95.
  • [4] Yu. M. Berezansky and Yu. G. Kondratiev, Spectral Methods in Infinite-Dimensional Analysis, (in Russian), Naukova Dumka, Kiev, 1988. English translation, Kluwer Academic Publishers, Dordrecht, 1995.
  • [5] Yu. M. Berezansky and E. V. Lytvynov, Generalized White Noise Analysis connected with pertubed field operators, Dopovidy AN Ukrainy, 10, (1993).
  • [6] Yu. M. Berezansky and S. N. Shifrin, The generalized degree symmetric Moment Problem, Ukrainian Math. J. 23 No 3, (1971), 247-258.
  • [7] N. Bourbaki, Elements of mathematics. Functions of a real variable. Addison-Wesley, 1976.
  • [8] Yu. L. Daletsky, A biorthogonal analogy of the Hermite polynomials and the inversion of the Fourier transform with respect to a non Gaussian measure, Funct. Anal. Appl. 25, (1991), 68-70.
  • [9] S. Dineen, Complex Analysis in Locally Convex Spaces, Mathematical Studies 57, North Holland, Amsterdam, 1981.
  • [10] I. M. Gefand, and N. Ya. Vilenkin, Generalized Functions, Vol. V, Academic Press, New York and London, 1968.
  • [11] T. Hida, Analysis of Brownian Functionals, Carleton Math. Lecture Notes No 13, 1975.
  • [12] T. Hida, Brownian Motion. Springer, New York, 1980.
  • [13] T. Hida, H. H. Kuo, J. Potthoff, and L. Streit, White Noise. An infinite dimensional calculus. Kluwer, Dordrecht, 1993.
  • [14] Y. Ito, Generalized Poisson Functionals, Prob. Th. Rel. Fields 77, (1988), 1-28.
  • [15] Y. Ito and I. Kubo, Calculus on Gaussian and Poisson White Noises. Nagoya Math. J. 111, (1988), 41-84.
  • [16] Yu. G. Kondratiev, (1978), Generalized functions in problems of infinite dimensional analysis. Ph.D. thesis, Kiev University.
  • [17] Yu. G. Kondratiev, Spaces of entire functions of an infinite number of variable, connected with the rigging of a Fock space. In: 'Spectral Analysis of Differential Operators.' Math. Inst. Acad. Sci. Ukrainian SSR, (1980), 18-37. English translation: Selecta Math. Sovietica 10 (1991), 165-180.
  • [18] Yu. G. Kondratiev, Nuclear spaces of entire functions in problems of infinite dimensional analysis. Soviet Math. Dokl. 22, (1980), 588-592.
  • [19] Yu. G. Kondratiev, P. Leukert, J. Potthoff, L. Streit, and W. Westerkamp, Generalized Functionals in Gaussian Spaces--the Characterization Theorem Revisited. J. Funct. Anal.141, No 2, (1996), 301-318.
  • [20] Yu. G. Kondratiev, P. Leukert, L. Streit, Wick Calculus in Gaussian Analysis, Acta Applicandae Mathematicae 44, (1996), 269-294.
  • [21] Yu. G. Kondratiev and Yu. S. Samoilenko, Spaces of trial and generalized functions of an infinite number of variables, Rep. Math. Phys. 14, No 3, (1978), 325-350.
  • [22] Yu. G. Kondratiev and L. Streit, Spaces of White Noise distributions: Constructions, Descriptions, Applications. I. Rep. Math. Phys. 33, (1993), 341-366.
  • [23] Yu. G. Kondratiev, L. Streit, and W. Westerkamp, A Note on Positive Distributions in Gaussian Analysis, Ukrainian Math. J. 47, No 5, (1995).
  • [24] Yu. G. Kondratiev and T. V. Tsykalenko, Dirichlet Operators and Associated Differential Equations. Selecta Math. Sovietica 10, (1991), 345-397.
  • [25] P. Kristensen, L. Mejlbo, and E. T. Poulsen, Tempered Distributions in Infinitely Many Dimensions. I. Canonical Field Operators. Commun. math. Phys. 1, (1965), 175-214.
  • [26] H.-H. Kuo, Lectures on white noise analysis. Soochow J. Math. 18, (1992), 229-300.
  • [27] Y.-J. Lee, Analytic Version of Test Functionals, Fourier Transform and a Characterization of Measures in White Noise Calculus. J. Funct. Anal. 100, (1991), 359-380.
  • [28] E. Lukacs, Characteristic Functions, 2nd edition, Griffin, London, 1970.
  • [29] B. Oksendal, Stochastic Partial Differential Equations and Applications to Hydrodynamics. In: 'Stochastic Analysis and Applications to Physics' Eds.: A. I. Cardoso et al, Kluwer, Dordrecht, 1995.
  • [30] H. Ouerdiane, Application des methodes d'holomorphie et de distributions en dimension quelconque a analyse sur les espaces Gaussiens. BiBoS preprint 491.
  • [31] J. Potthoff, On positive generalized functionals. J. Funct. Anal. 74, (1987), 81-95.
  • [32] J. Potthoff and L. Streit, A characterization of Hida distributions. J. Funct. Anal. 101, (1991), 212-229.
  • [33] H. H. Schaefer, Topological Vector Spaces, Springer, New York, 1971.
  • [34] A. V. Skorohod, Integration in Hubert Space, Springer, Berlin, 1974.
  • [35] G. Vage, (1995), Stochastic Differential Equations and Kondratiev Spaces. Ph.D. thesis, Trondheim University.
  • [36] A. M. Vershik, I. M. Gelfand, and M. I. Graev, Representations of diffeomorphisms groups. Russian Math. Surveys 30, No 6, (1975), 3-50.
  • [37] Y. Yokoi, Positive generalized white noise functionals. Hiroshima Math. J. 20, (1990), 137-157.
  • [38] Y. Yokoi, Simple setting for white noise calculus using Bargmann space and Gauss transform. Hiroshima Math. J. 25, No 1, (1995), 97-121.