2008 | OriginalPaper | Chapter
Image of a Jacobi Field
Authors : Yurij M. Berezansky, Artem D. Pulemyotov
Published in: Recent Advances in Matrix and Operator Theory
Publisher: Birkhäuser Basel
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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-Itô decomposition for ρK. Finally, we illustrate our constructions by offering a few examples and exploring a relatively transparent special case.