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Mat. Zametki, 2006, Volume 79, Issue 3, Pages 362–368 (Mi mz2706)  

This article is cited in 5 scientific papers (total in 5 papers)

A generalization of the Beurling–Lax theorem

B. V. Vinnitskii, V. N. Dil'nyi

Ivan Franko National University of L'viv

Abstract: We obtain conditions for the completeness of the system $\{G(z)e^{\tau z},\tau\leqslant0\}$ in the space $H^2_\sigma(\mathbb C_+)$, $0<\sigma<+\infty$, of functions analytic in the right-hand half-plane for which
$$ \|f\|:=\sup_{-\pi/2<\varphi<\pi/2}\{ \int_0^{+\infty}|f(re^{i\varphi})|^2e^{-2r\sigma|\sin\varphi|} dr\}^{1/2}<+\infty. $$


DOI: https://doi.org/10.4213/mzm2706

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English version:
Mathematical Notes, 2006, 79:3, 335–341

Bibliographic databases:

UDC: 517.1
Received: 27.10.2004
Revised: 21.06.2005

Citation: B. V. Vinnitskii, V. N. Dil'nyi, “A generalization of the Beurling–Lax theorem”, Mat. Zametki, 79:3 (2006), 362–368; Math. Notes, 79:3 (2006), 335–341

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Dil'nyi V.M., “Equivalent definition of some weighted Hardy spaces”, Ukrainian Math. J., 60:9 (2008), 1477–1482  crossref  mathscinet  isi  scopus
    2. V. Dilnyi, “On cyclic functions in weighted Hardy spaces”, Zhurn. matem. fiz., anal., geom., 7:1 (2011), 19–33  mathnet  mathscinet  zmath  elib
    3. B. V. Vinnitskii, V. N. Dilnyi, “On generalization of Paley-Wiener theorem for weighted Hardy spaces”, Ufa Math. J., 5:4 (2013), 30–36  mathnet  crossref  elib
    4. V. N. Dilnyi, “Splitting of some spaces of analytic functions”, Ufa Math. J., 6:2 (2014), 25–34  mathnet  crossref  elib
    5. 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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