Infinite dimensional Gegenbauer functionals
Volume 78 / 2007
Banach Center Publications 78 (2007), 35-45
MSC: Primary 60H40; Secondary 46A32, 46F25, 46G20.
DOI: 10.4064/bc78-0-2
Abstract
he paper is devoted to investigation of Gegenbauer white noise functionals. A particular attention is paid to the construction of the infinite dimensional Gegenbauer white noise measure ${\mathcal{G}}_{\beta}$, via the Bochner-Minlos theorem, on a suitable nuclear triple. Then we give the chaos decomposition of the $L^{2}$-space with respect to the measure ${\mathcal{G}}_{\beta}$ by using the so-called $\beta$-type Wick product.
