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# On Kondratiev spaces of test functions in the non-Gaussian infinite-dimensional analysis

### Abstract

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 $Q\times H \ni (x,\lambda)\mapsto h(x;\lambda)\in\mathbb C$, where $Q$ is a metric space, $H$ is some complex Hilbert space, $h$ satisfies certain assumptions (in particular, $h(\cdot;\lambda)$ is a continuous function, $h(x;\cdot)$ 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 $\gamma(\lambda)h(x;\alpha(\lambda))$, where $\gamma :H\to\mathbb C$ and $\alpha :H\to H$ 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.

Key words: Kondratiev space, non-Gaussian analysis.

### Article Information

 Title On Kondratiev spaces of test functions in the non-Gaussian infinite-dimensional analysis Source Methods Funct. Anal. Topology, Vol. 19 (2013), no. 4, 301-309 MathSciNet MR3156296 zbMATH 1313.46048 Milestones Received 30/08/2013; Revised 17/09/2013 Copyright The Author(s) 2013 (CC BY-SA)

### Authors Information

N. A. Kachanovsky
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

### Citation Example

N. A. Kachanovsky, On Kondratiev spaces of test functions in the non-Gaussian infinite-dimensional analysis, Methods Funct. Anal. Topology 19 (2013), no. 4, 301-309.

### BibTex

@article {MFAT705,
AUTHOR = {Kachanovsky, N. A.},
TITLE = {On Kondratiev spaces of test functions in the non-Gaussian infinite-dimensional analysis},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {19},
YEAR = {2013},
NUMBER = {4},
PAGES = {301-309},
ISSN = {1029-3531},
MRNUMBER = {MR3156296},
ZBLNUMBER = {1313.46048},
URL = {http://mfat.imath.kiev.ua/article/?id=705},
}