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Mat. Zametki, 1976, Volume 19, Issue 4, Pages 491–500 (Mi mz7767)  

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

Boundary values of a convergent sequence of J-contractive matrix-functions

D. Z. Arova, L. A. Simakovab

a Odessa Pedagogical Institute
b Odessa Technological Institute for Refrigeration Industry

Abstract: In this note it is proved that if $W_n(z)$ are $J$-contractive matrix-functions which are meromorphic in the disk $|z|<1$ ($J-W_n^*(z)JW_n(z)\ge0$, $J^*=J$, $J^2=I$), $W_n(z)\to W(z)$, as $n\to\infty$,
$$ W^*(z)JW(z)\le W_n^*(z)JW_n(z) $$
and
$$ \det W(z)\not\equiv0, $$
then there exists a subsequence $W_{n_k}(z)$ whose boundary values
$$ W^*_{n_k}(\zeta)JW_{n_k}(\zeta)\to W^*(\zeta)JW(\zeta)\quad (a. e. |\zeta|=1). $$
It follows from this result that every convergent Blaschke–Potapov product has $J$-unitary boundary values.

Full text: PDF file (747 kB)

English version:
Mathematical Notes, 1976, 19:4, 301–306

Bibliographic databases:

UDC: 517.5
Received: 11.11.1974

Citation: D. Z. Arov, L. A. Simakova, “Boundary values of a convergent sequence of J-contractive matrix-functions”, Mat. Zametki, 19:4 (1976), 491–500; Math. Notes, 19:4 (1976), 301–306

Citation in format AMSBIB
\Bibitem{AroSim76}
\by D.~Z.~Arov, L.~A.~Simakova
\paper Boundary values of a convergent sequence of J-contractive matrix-functions
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 4
\pages 491--500
\mathnet{http://mi.mathnet.ru/mz7767}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=486555}
\zmath{https://zbmath.org/?q=an:0346.15004|0335.15027}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 4
\pages 301--306
\crossref{https://doi.org/10.1007/BF01156787}


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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. D. Z. Arov, “Regular and singular $J$-inner matrix-functions and the corresponding interpolation problems”, Funct. Anal. Appl., 22:1 (1988), 46–48  mathnet  crossref  mathscinet  zmath  isi
  • Математические заметки Mathematical Notes
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