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osu1054787409.pdf (509.87 KB)
ETD Abstract Container
Abstract Header
Characterization of operators in non-gaussian infinite dimensional analysis
Author Info
Yablonsky, Eugene
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1054787409
Abstract Details
Year and Degree
2003, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
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.
Committee
Alexander Dynin (Advisor)
Pages
108 p.
Subject Headings
Mathematics
Keywords
White Noise Operators
;
Biorthogonal Appell systems
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Citations
Yablonsky, E. (2003).
Characterization of operators in non-gaussian infinite dimensional analysis
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1054787409
APA Style (7th edition)
Yablonsky, Eugene.
Characterization of operators in non-gaussian infinite dimensional analysis.
2003. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1054787409.
MLA Style (8th edition)
Yablonsky, Eugene. "Characterization of operators in non-gaussian infinite dimensional analysis." Doctoral dissertation, Ohio State University, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=osu1054787409
Chicago Manual of Style (17th edition)
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Document number:
osu1054787409
Download Count:
806
Copyright Info
© 2003, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.