Abstract
A general theory of operators on vector-valued white noise functionals is established in line with Hid′s white noise calculus. A basic role is played by an integral kernel operator which is a superposition of creation and annihilation operators with operator-valued distributions as integral kernel. The symbol of a continuous operator on vector-valued white noise functionals is characterized by its analyticity and boundedness. A significant consequence is that every continuous operator on vector-valued white noise functionals admits an infinite series expansion in terms of integral kernel operators with precise estimate of the convergence.
Original language | English |
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Pages (from-to) | 185-232 |
Number of pages | 48 |
Journal | Journal of Functional Analysis |
Volume | 121 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1994 Apr |
Externally published | Yes |
ASJC Scopus subject areas
- Analysis