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Fundam. Prikl. Mat., 2006, Volume 12, Issue 5, Pages 221–236 (Mi fpm984)  

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

Weighted Schur class functions and functional model

A. S. Tikhonov

Vernadskiy Tavricheskiy National University

Abstract: We generalize the class of contractive valued, analytic in the unit disk functions (Schur class) to the case of finitely connected domains with operator valued weights on the boundary. The two fundamental decompositions (the inner-outer factorization and the decomposition into an orthogonal sum of the pure and the unitary parts) are extended to our setting. This generalization allows to use an uniform approach to functional models developed recently in papers of the author and D. Yakubovich. Moreover, it gives an alternative language to handle multiply-valued functions in the multiply-connected case.

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English version:
Journal of Mathematical Sciences (New York), 2008, 150:6, 2609–2619

Bibliographic databases:

UDC: 517.547+517.983

Citation: A. S. Tikhonov, “Weighted Schur class functions and functional model”, Fundam. Prikl. Mat., 12:5 (2006), 221–236; J. Math. Sci., 150:6 (2008), 2609–2619

Citation in format AMSBIB
\Bibitem{Tik06}
\by A.~S.~Tikhonov
\paper Weighted Schur class functions and functional model
\jour Fundam. Prikl. Mat.
\yr 2006
\vol 12
\issue 5
\pages 221--236
\mathnet{http://mi.mathnet.ru/fpm984}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2314126}
\zmath{https://zbmath.org/?q=an:1151.30331}
\transl
\jour J. Math. Sci.
\yr 2008
\vol 150
\issue 6
\pages 2609--2619
\crossref{https://doi.org/10.1007/s10958-008-0159-0}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-42449147099}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Tikhonov A., “Inner-Outer Factorization for Weighted Schur Class Functions and Corresponding Invariant Subspaces”, Spectral Theory and Analysis, Operator Theory Advances and Applications, 214, eds. Janas J., Kurasov P., Laptev A., Naboko S., Stolz G., Birkhauser Verlag Ag, 2011, 125–134  mathscinet  isi
  • Фундаментальная и прикладная математика
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