White Noise pp 146-183 | Cite as

Calculus of Differential Operators

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


This chapter is devoted to the theory of differentiation of — and differential operators acting on — functionals of white noise. On one hand the ideas are very much inspired by the work of P. Lévy (in particular Lévy (1951)), and on the other hand by the theory of creation and annihilation operators on Fock space (e.g., Berezin (1966)). Background references for this chapter are, Hida (1975a), Kubo and Takenaka (1980b), Kuo (1983d), Potthoff and Yan (1992), and for the general theory of Gâteaux and Fréchet derivatives, e.g., the book of Schwartz (1969).

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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