Image of a Jacobi Field

Berezansky, Yurij M. and Pulemotov, Artem (2008). Image of a Jacobi Field. In Joseph A. Ball, Yuli. Eidelman, J. William Helton, Vadim Olshevsky and J.ames Rovnyak (Ed.), Recent advances in matrix and operator theory (pp. 47-62) Basel, Switzerland: Birkhauser Verlag.

Author Berezansky, Yurij M.
Pulemotov, Artem
Title of chapter Image of a Jacobi Field
Title of book Recent advances in matrix and operator theory
Place of Publication Basel, Switzerland
Publisher Birkhauser Verlag
Publication Year 2008
Sub-type Chapter in textbook
Series Operator theory: Advances and applications
ISBN 9783764385392
3764385391
9783764385385
3764385383
ISSN 0255-0156
Editor Joseph A. Ball
Yuli. Eidelman
J. William Helton
Vadim Olshevsky
J.ames Rovnyak
Volume number 179
Chapter number 4
Start page 47
End page 62
Total pages 16
Total chapters 19
Collection year 2008
Language eng
Formatted Abstract/Summary
Consider the two Hilbert spaces H− and T−. Let K+ : H− → T− be a bounded operator. Consider a measure ρ on H−. Denote by ρK the image of the measure ρ under K+. This paper aims to study the measure ρK assuming ρ to be the spectral measure of a Jacobi field. We present a family of operators whose spectral measure equals ρK. We state an analogue of the Wiener-Itˆo decompos ition for ρK. Finally, we illustrate our constructions by offering a few examples and exploring a relatively transparent special case.
Keyword Image measure
Jacobi field
Spectral measure
Q-Index Code BX
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Book Chapter
Collection: School of Mathematics and Physics
 
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Created: Thu, 18 Oct 2012, 15:36:00 EST by Kay Mackie on behalf of School of Mathematics & Physics