Spectral theory and Wiener-Itô decomposition for the image of a Jacobi field
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Assume that K +: H − → T − is a bounded operator, where H − and T − are Hilbert spaces and ρ is a measure on the space H −. Denote by ρK the image of the measure ρ under K +. We study the measure ρK under the assumption that ρ is the spectral measure of a Jacobi field and obtain a family of operators whose spectral measure is equal to ρK. We also obtain an analog of the Wiener-Itô decomposition for ρK. Finally, we illustrate the results obtained by explicit calculations carried out for the case, where ρK is a Lévy noise measure.
KeywordsOrthogonal Polynomial Noise Measure Spectral Measure Spectral Theory Gaussian Measure
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- 17.C. F. Dunkl and Xu Yuan, “Orthogonal polynomials of several variables,” Encycl. Math. Appl., 81 (2001).Google Scholar
- 18.Yu. M. Berezansky and Yu. G. Kondratiev, Spectral Methods in Infinite-Dimensional Analysis, Kluwer, Dordrecht (1995).Google Scholar
- 27.W. Schoutens, “Stochastic processes and orthogonal polynomials,” Lect. Notes Statist., 146 (2000).Google Scholar