Kondratiev, Yu. G., Streit, L., Westerkamp, W., and Yan, J.-A.: Generalized functions in infinite dimensional analysis; Hiroshima Math. J. 28 (1998) 213--260  Home/Search   Document Details and Download   Summary   Related Articles   Check

....defined on some neighborhood of 0 2 E c . Therefore, the growth conditions in Theorems 3.4 and 3.6 need to be stated in different ways. For characterization CHARACTERIZATION THEOREMS, INTRINSIC TOPOLOGIES 27 theorems with the S transform only defined on a neighborhood of 0, see the papers [5] [12]. In order to get more information for the Gel fand triple [E ] u ae (L 2 ) ae [E ] u , we may still want to consider u from some subsets of C ;log . For example, let C ;1=k ; k 0; consist of all positive continuous functions u on [0; 1) such that lim r 1 log u(r) r 1=k = 1: ....

Kondratiev, Yu. G., Streit, L., Westerkamp, W., and Yan, J.-A.: Generalized functions in infinite dimensional analysis; Hiroshima Math. J. 28 (1998) 213--260

....of the Ukrainian National Science Academy, 3 Tereshchenkivs ka St, 252601, Kyiv, Ukraine; e mails: mathkiev imat.gluk.apc.org, rebenko physik.uni bielefeld.de, gena imat.gluk.apc.org, shchepan physik.uni bielefeld.de. 2 LYTVYNOV, REBENKO, AND SHCHEPAN UK There is also another approach [1, 24] to the construction and investigation of spaces of test and generalized non Gaussian functions, where one uses a system of Appell polynomials and its dual system. But as shown in [39] see also [6, 31] in case of the measure P , it leads actually to the same triple (1.3) The aim of the ....

....i Gamma1 : hh Phi; OEii = 0; OE 2 (SCP ) 1 Psi : So, we will derive some results for generalized functions of CPWN from the corresponding results for the usual one, taking the factor space structure into account. We will apply also to the space (L 2 CP ) the method of biorthogonal analysis [24] and compare it with the Fock space method. Just as in the case of the usual Poisson, it turns out that the method of [24] leads to the same triple (SCP ) Gamma1 oe (L 2 CP ) oe (SCP ) 1 ; 1.6) which gives, particularly, the inner description of (SCP ) 1 . Our special attention will be ....

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Yu. G. Kondratiev, L. Streit, W. Westerkamp, J. Yan, Generalized functions in infinite dimensional analysis, Preprint, BiBoS University, Bielefeld, 1995.

.... notation for the distribution introduced above) Any Phi 2 P 0 (N 0 ) then has the unique decomposition Phi = 1 X n=0 h: x Omega n : Phi (n) i; 5) where the sum converges in P 0 (N 0 ) and we have hh Phi; ii = 1 X n=0 n h Phi (n) n) i; 2 P(N 0 ) 6) see [KSWY95] 4.2 Spaces of generalized functions In order to construct the spaces of test functions we define for any given p; q 2 N 0 ; fi 2 [0; 1] the following Hilbertian norm for the smooth Wick polynomials (x) P N n=0 h: x Omega n : n) i; x 2 N 0 : k k 2 p;q;fi : 1 X n=0 ....

Yu.G. Kondratiev, L. Streit, W. Westerkamp, and J.-A. Yan. Generalized Functions in Infinite Dimensional Analysis. IIAS Reports 1995-002, International Institute for Advanced Studies, Kyoto, 1995. To appear in Hiroshima Math. J.

.... da Madeira, P 9000 Funchal, Portugal Ludwig Streit BiBoS, Universitat Bielefeld, D 33615 Bielefeld, Germany CCM, Universidade da Madeira, P 9000 Funchal, Portugal May 29, 1996 Abstract We give a general approach to infinite dimensional non Gaussian analysis which generalizes the work [KSWY95]. For given measure we construct a family of biorthogonal systems. We study their properties and their Gel fand triples that they generate. As an example we consider the measures of Poisson type. Contents 1 Introduction 3 2 General theory 5 2.1 Some facts on nuclear triples : ....

....Yu. L. Daletskii [Da91] For a detailed description of its use in infinite dimensional analysis and for the proof of the results which were announced in [AKS93] we refer to [ADKS96] which was based on quasi invariance of the measures and smoothness of the logarithmic derivatives. Kondratiev et al. [KSWY95] considered the case of non degenerate measures on the dual of a nuclear space with analytic characteristic functionals and no further conditions such as quasi invariance of the measure or smoothness of the logarithmic derivative was required. In this case the important example of Poisson noise is ....

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Kondratiev, Yu.G., Streit, L., Westerkamp, W. and Yan, J.-A. (1995), Generalized Functions in Infinite Dimensional Analysis. Submitted to Hiroshima Mathematical Journal.

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