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Mat. Sb., 2002, Volume 193, Number 6, Pages 143–160 (Mi msb664)  

This article is cited in 7 scientific papers (total in 7 papers)

Weakly invertible elements in anisotropic weighted spaces of holomorphic functions in a polydisc

F. A. Shamoyan

I. G. Petrovsky Bryansk State Pedagogical University

Abstract: The question of weak invertibility is studied in weighted $L^p$-spaces of holomorphic functions in a polydisc. A complete description of weight functions such that each non-vanishing bounded holomorphic function in a polydisc is weakly invertible in the corresponding spaces is obtained. In addition, it is shown for $n\geqslant 2$ that, by contrast with the one-dimensional case, the weak invertibility of outer functions is equivalent in a certain sense to the weak invertibility of inner functions.

DOI: https://doi.org/10.4213/sm664

Full text: PDF file (309 kB)
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English version:
Sbornik: Mathematics, 2002, 193:6, 925–943

Bibliographic databases:

UDC: 517.55
MSC: Primary 32A37; Secondary 46E15
Received: 15.01.2001

Citation: F. A. Shamoyan, “Weakly invertible elements in anisotropic weighted spaces of holomorphic functions in a polydisc”, Mat. Sb., 193:6 (2002), 143–160; Sb. Math., 193:6 (2002), 925–943

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm664
  • http://mi.mathnet.ru/eng/msb/v193/i6/p143

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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. F. A. Shamoyan, “On the cyclic elements of the shift operator in a weighted anisotropic space of holomorphic function in the polydisc”, J. Math. Sci. (N. Y.), 139:2 (2006), 6491–6495  mathnet  crossref  mathscinet  zmath  elib
    2. F. A. Shamoyan, “Weakly invertible elements of weighted $L^p$-spaces of holomorphic functions”, Russian Math. Surveys, 64:1 (2009), 165–167  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. F. A. Shamoyan, “A weak invertibility criterion in the weighted $L^p$-spaces of holomorphic functions in the ball”, Siberian Math. J., 50:6 (2009), 1115–1132  mathnet  crossref  mathscinet  isi  elib  elib
    4. Nikolski N., “In a Shadow of the Rh: Cyclic Vectors of Hardy Spaces on the Hilbert Multidisc”, Ann. Inst. Fourier, 62:5 (2012), 1601–1626  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    5. F. A. Shamoyan, “On Polynomial Approximation in Anisotropic Weighted Spaces of Holomorphic Functions in a Polydisc”, Complex Anal. Oper. Theory, 2014  crossref  mathscinet  scopus  scopus  scopus
    6. F. A. Shamoyan, “On a class of inner functions in a half-space”, Ufa Math. J., 7:4 (2015), 127–139  mathnet  crossref  isi  elib
    7. F. A. Shamoyan, “Fourier transform and quasi-analytic classes of functions of bounded type on tubular domains”, Funct. Anal. Appl., 51:2 (2017), 157–160  mathnet  crossref  crossref  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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