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In this chapter we construct spaces of generalized functionals on N*. Generalized functions over infinite dimensional spaces have applications in various domains. They appear in hydrodynamics and turbulence theory (e.g., Chow (1989), Lindstrøm et al. (1991)), quantum mechanics (Hida and Streit (1983), de Faria et al. (1990)), quantum field theory (Albeverio, Hida et al. (1990a), Potthoff and Streit (1990)), potential theory in infinite dimensions (Albeverio, Hida et al. (1990b), Hida, Potthoff, and Streit (1988), Potthoff and Röckner (1990), Potthoff and Streit (1990)), the theory of anticipating stochastic differential equations (Kuo and Potthoff (1990)), non-linear filtering (Hida (1975b)), in Malliavin calculus (e.g., Watanabe (1983), Sugita (1985), Potthoff (1988)), in the theory of stochastic partial differential equations (Chow (1989b), Nualart and Zakai (1989)).
KeywordsWhite Noise Generalize Functional Quantized Operator Integral Kernel Projective Limit
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