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Mat. Sb., 2016, Volume 207, Number 7, Pages 57–80 (Mi msb8534)  

This article is cited in 3 scientific papers (total in 3 papers)

Spectral analysis on the group of conformal automorphisms of the unit disc

V. V. Volchkov, Vit.V.Volchkov

Donetsk National University, Ukraine

Abstract: For the group $G$ of conformal automorphisms of the unit disc the problem of spectral analysis is considered for subspaces $\mathscr{U}\subset C(G)$ which are invariant under right shifts by elements of $G$ and conjugations by elements of the rotation subgroup. It turns out that, in contrast to subspaces of $C(G)$ which are merely invariant under right shifts, $\mathscr{U}$ contains a minimal subspace with the above properties.
Bibliography: 26 titles.

Keywords: spectral analysis, conformal automorphism group, invariant subspace, Schwartz theorem.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8534

Full text: PDF file (635 kB)
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English version:
Sbornik: Mathematics, 2016, 207:7, 942–963

Bibliographic databases:

UDC: 517.444
MSC: 43A45
Received: 29.04.2015 and 02.04.2016

Citation: V. V. Volchkov, Vit.V.Volchkov, “Spectral analysis on the group of conformal automorphisms of the unit disc”, Mat. Sb., 207:7 (2016), 57–80; Sb. Math., 207:7 (2016), 942–963

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm8534
  • http://mi.mathnet.ru/eng/msb/v207/i7/p57

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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. V. V. Volchkov, Vit. V. Volchkov, “Spectral synthesis on the group of conformal automorphisms of the unit disc”, Sb. Math., 209:1 (2018), 1–34  mathnet  crossref  crossref  adsnasa  isi  elib
    2. V. V. Volchkov, Vit. V. Volchkov, “An Analog of the Brown–Schreiber–Taylor Theorem for Weighted Hyperbolic Shifts”, Math. Notes, 103:2 (2018), 175–186  mathnet  crossref  crossref  isi  elib
    3. V. V. Volchkov, Vit. V. Volchkov, “A new characterization of holomorphic functions in the unit disk”, Probl. anal. Issues Anal., 7(25):1 (2018), 134–147  mathnet  crossref  elib
  •  Sbornik: Mathematics (from 1967)
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