Infinite dimensional Gegenbauer functionals

Abstract

Abstract. The 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 G β , 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 G β by using the so-called β-type Wick product.

The q-Gamma White Noise

“…Nowadays, this theory has been applied to stochastic integration, stochastic partial differential equation, stochastic variational equation, infinite dimensional harmonic analysis, Dirichlet forms, quantum field theory, Feynman integral and quantum probability. For the non-Gaussian white noise analysis, Y. I t o constructed the Poissonian counterpart of Hida's theory and K o n d r a t i e v et al [8] established a purely non-Gaussian distribution theory in infinite dimensional analysis by means of a normalized Laplace transform, and B a r h o u m i et al [1] developed the introduction of infinite dimensional Gegenbauer white noise.…”