On Kondratiev spaces of test functions in the non-Gaussian infinite-dimensional analysis - Kachanovsky, N. A. (Methods of Functional Analysis and Topology, 2013)
A blanket version of the non-Gaussian analysis under the so-called bior hogo al approach uses the Kondratiev spaces of test functions with orthogonal bases given by a generating function Q× H i (x,λ)h(x;λ)C, where Q is a metric space, H is some complex Hilbert space, h satisfies certain assumptions (in particular, h(·;λ) is a continuous function, h(x;·) is a holomorphic at zero function). In this paper we consider the construction of the Kondratiev spaces of test functions with orthogonal bases given by a generating function γ(λ)h(x;α(λ)), where γ :H→C and α :H→ H are holomorphic at zero functions, and study some properties of these spaces. The results of the paper give a possibility to extend an area of possible applications of the above mentioned theory.