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Ukrainian Mathematical Journal

, Volume 59, Issue 6, pp 811–832 | Cite as

Spectral theory and Wiener-Itô decomposition for the image of a Jacobi field

  • Yu. M. Berezansky
  • A. D. Pulemyotov
Article
  • 32 Downloads

Abstract

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.

Keywords

Orthogonal Polynomial Noise Measure Spectral Measure Spectral Theory Gaussian Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • Yu. M. Berezansky
    • 1
  • A. D. Pulemyotov
    • 2
  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKyiv
  2. 2.Cornell UniversityIthacaUSA

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