Open Access

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.


Full Text





Article Information

TitleOn Kondratiev spaces of test functions in the non-Gaussian infinite-dimensional analysis
SourceMethods Funct. Anal. Topology, Vol. 19 (2013), no. 4, 301-309
MathSciNet MR3156296
zbMATH 1313.46048
MilestonesReceived 30/08/2013; Revised 17/09/2013
CopyrightThe 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 


Google Scholar Metrics

Citing articles in Google Scholar
Similar articles in Google Scholar

Export article

Save to Mendeley



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},
}


All Issues