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White Noise pp 35-73 | Cite as

Generalized Functionals

  • Takeyuki Hida
  • Hui-Hsiung Kuo
  • Jürgen Potthoff
  • Ludwig Streit
Chapter
  • 402 Downloads
Part of the Mathematics and Its Applications book series (MAIA, volume 253)

Abstract

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)).

Keywords

White Noise Generalize Functional Quantized Operator Integral Kernel Projective Limit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  • Takeyuki Hida
    • 1
  • Hui-Hsiung Kuo
    • 2
  • Jürgen Potthoff
    • 3
  • Ludwig Streit
    • 4
    • 5
  1. 1.Department of MathematicsMeijo UniversityNagoyaJapan
  2. 2.Department of MathematicsLouisiana State UniversityBaton RougeUSA
  3. 3.Universität MannheimMannheimGermany
  4. 4.BiBos, Universität BielefeldBielefeldGermany
  5. 5.Universidade da MadeiraFunchal, MadeiraPortugal

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