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Characterization of operators in non-gaussian infinite dimensional analysis
Yablonsky, Eugene

2003, Doctor of Philosophy, Ohio State University, Mathematics.
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.
Alexander Dynin (Advisor)
108 p.

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Yablonsky, E. (2003). Characterization of operators in non-gaussian infinite dimensional analysis. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Yablonsky, Eugene. "Characterization of operators in non-gaussian infinite dimensional analysis." Electronic Thesis or Dissertation. Ohio State University, 2003. OhioLINK Electronic Theses and Dissertations Center. 26 Sep 2017.

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Yablonsky, Eugene "Characterization of operators in non-gaussian infinite dimensional analysis." Electronic Thesis or Dissertation. Ohio State University, 2003. https://etd.ohiolink.edu/

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