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Ufimsk. Mat. Zh., 2012, Volume 4, Issue 1, Pages 17–28 (Mi ufa128)  

This article is cited in 1 scientific paper (total in 1 paper)

Applications of model spaces to construction of cocyclic perturbations of a semigroup of shifts on a semiaxis

G. G. Amosova, A. D. Baranovb, V. V. Kapustinc

a Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia
b St. Petersburg State University, St. Petersburg, Russia
c St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia

Abstract: We describe a construction of cocyclic perturbations of the semigroup of shifts on the half-line by means of theory of model spaces. It is shown that one can choose an inner function that determines the model space so that the elements of the perturbed semigroup have a prescribed spectral type and differ from the elements of the initial semigroup by operators from the Schatten–von Neumann class $\mathfrak S_p$, $p>1$. The case of the trace class $\mathfrak S_1$ perturbations is considered separately.

Keywords: semigroup of shifts, inner function, Schatten–von Neumann classes.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00584-a
Russian Academy of Sciences - Federal Agency for Scientific Organizations


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Bibliographic databases:
UDC: 517.9
Received: 20.12.2011

Citation: G. G. Amosov, A. D. Baranov, V. V. Kapustin, “Applications of model spaces to construction of cocyclic perturbations of a semigroup of shifts on a semiaxis”, Ufimsk. Mat. Zh., 4:1 (2012), 17–28

Citation in format AMSBIB
\Bibitem{AmoBarKap12}
\by G.~G.~Amosov, A.~D.~Baranov, V.~V.~Kapustin
\paper Applications of model spaces to construction of cocyclic perturbations of a~semigroup of shifts on a~semiaxis
\jour Ufimsk. Mat. Zh.
\yr 2012
\vol 4
\issue 1
\pages 17--28
\mathnet{http://mi.mathnet.ru/ufa128}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3435429}
\elib{http://elibrary.ru/item.asp?id=18877628}


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    This publication is cited in the following articles:
    1. Dil'nyi V.M., “on Invariant Subspaces in Weighted Hardy Spaces”, Ukr. Math. J., 66:6 (2014), 955–960  crossref  mathscinet  zmath  isi  scopus
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