Characterization of operators in non-gaussian infinite dimensional analysis

Bibliographic Details
Main Author:	Yablonsky, Eugene
Language:	English
Published:	The Ohio State University / OhioLINK 2003
Subjects:	Mathematics White Noise Operators Biorthogonal Appell systems
Online Access:	http://rave.ohiolink.edu/etdc/view?acc_num=osu1054787409

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spelling	ndltd-OhioLink-oai-etd.ohiolink.edu-osu10547874092021-08-03T05:48:08Z Characterization of operators in non-gaussian infinite dimensional analysis Yablonsky, Eugene Mathematics White Noise Operators Biorthogonal Appell systems It is known that many constructions arising in the classical Gaussian infinite dimensional analysis can be extended to the case of more general measures. One of such extensions can be obtained through biorthogonal systems of polynomials and generalized functions. That approach was discussed by Yu. Daletsky, S. Albeverio, Yu. Kondratiev, L.Streit, W. Westerkamp, J.-A. Yan, J. Silva, et al., who considered a broad class of non-degenerate measures with analytic characteristic functionals. In this thesis we develop a theory of white noise operators, i.e., linear continuous operators from a nuclear Fréchet space of test functionals to its dual space in this more general setting. We construct an isometric integral transform of those operators into the space of germs of holomorphic functions on a locally convex infinite dimensional nuclear space. Using such transform we provide characterization theorems and consider the biorthogonal chaos expansion for white noise operators. We also provide a biorthogonal construction for integral kernel operators, and show that any white noise operator can be represented by a strongly convergent series of those integral kernel operators. In addition, we discuss various examples of spaces of test functions in infinite dimensional analysis and relations among them. 2003-09-05 English text The Ohio State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=osu1054787409 http://rave.ohiolink.edu/etdc/view?acc_num=osu1054787409 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
collection	NDLTD
language	English
sources	NDLTD
topic	Mathematics White Noise Operators Biorthogonal Appell systems
spellingShingle	Mathematics White Noise Operators Biorthogonal Appell systems Yablonsky, Eugene Characterization of operators in non-gaussian infinite dimensional analysis
author	Yablonsky, Eugene
author_facet	Yablonsky, Eugene
author_sort	Yablonsky, Eugene
title	Characterization of operators in non-gaussian infinite dimensional analysis
title_short	Characterization of operators in non-gaussian infinite dimensional analysis
title_full	Characterization of operators in non-gaussian infinite dimensional analysis
title_fullStr	Characterization of operators in non-gaussian infinite dimensional analysis
title_full_unstemmed	Characterization of operators in non-gaussian infinite dimensional analysis
title_sort	characterization of operators in non-gaussian infinite dimensional analysis
publisher	The Ohio State University / OhioLINK
publishDate	2003
url	http://rave.ohiolink.edu/etdc/view?acc_num=osu1054787409
work_keys_str_mv	AT yablonskyeugene characterizationofoperatorsinnongaussianinfinitedimensionalanalysis
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Characterization of operators in non-gaussian infinite dimensional analysis

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