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Izv. RAN. Ser. Mat., 2007, Volume 71, Issue 6, Pages 69–90 (Mi izv694)  

This article is cited in 12 scientific papers (total in 12 papers)

The absence of unconditional bases of exponentials in Bergman spaces on non-polygonal domains

K. P. Isaev, R. S. Yulmukhametov

Bashkir State University

Abstract: We prove that it is impossible to construct unconditional bases of exponentials in the Bergman space $B_2(D)$ in the case when $D$ is a bounded convex domain on the plane such that at some point of the boundary the curvature exists and is different from zero.

DOI: https://doi.org/10.4213/im694

Full text: PDF file (536 kB)
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English version:
Izvestiya: Mathematics, 2007, 71:6, 1145–1166

Bibliographic databases:

UDC: 517.54
MSC: 30B60, 30D15
Received: 10.03.2005

Citation: K. P. Isaev, R. S. Yulmukhametov, “The absence of unconditional bases of exponentials in Bergman spaces on non-polygonal domains”, Izv. RAN. Ser. Mat., 71:6 (2007), 69–90; Izv. Math., 71:6 (2007), 1145–1166

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. Borichev A., Lyubarskii Yu., “Riesz bases of reproducing kernels in Fock-type spaces”, J. Inst. Math. Jussieu, 9 (2010), 449–461  crossref  mathscinet  zmath  isi  elib  scopus
    2. K. P. Isaev, “Bazisy Rissa iz eksponent v prostranstvakh Bergmana na vypuklykh mnogougolnikakh”, Ufimsk. matem. zhurn., 2:1 (2010), 71–86  mathnet  zmath  elib
    3. K. P. Isaev, R. S. Yulmukhametov, “Unconditional exponential bases in Hilbert spaces”, Ufa Math. J., 3:1 (2011), 3–15  mathnet  mathscinet  zmath
    4. K. P. Isaev, R. S. Yulmukhametov, “Unconditional bases of reproducing kernels in Hilbert spaces of entire functions”, Ufa Math. J., 5:3 (2013), 67–76  mathnet  crossref  elib
    5. Dumont A., Kellay K., “Convergence of Lagrange Interpolation Series in the Pock Spaces”, Publ. Mat., 58:1 (2014), 121–132  crossref  mathscinet  zmath  isi
    6. A. Baranov, A. Dumont, A. Hartmann, K. Kellay, “Sampling, interpolation and Riesz bases in small Fock spaces”, Journal de Mathématiques Pures et Appliquées, 2014  crossref  mathscinet  scopus
    7. A. A. Yunusov, “On unconditional exponential bases in weighted spaces on real axis”, Ufa Math. J., 7:3 (2015), 108–118  mathnet  crossref  isi  elib
    8. K. P. Isaev, R. S. Yulmukhametov, A. A. Yunusov, “On unconditional exponential bases in weighted spaces on interval of real axis”, St. Petersburg Math. J., 28:5 (2017), 689–706  mathnet  crossref  mathscinet  isi  elib
    9. Isaev K.P., “On unconditional exponential bases in weighted spaces on interval of real axis”, Lobachevskii J. Math., 38:1 (2017), 48–61  crossref  mathscinet  zmath  isi  scopus
    10. K. P. Isaev, K. V. Trounov, R. S. Yulmukhametov, “Representing systems of exponentials in projective limits of weighted subspaces of $H(D)$”, Izv. Math., 83:2 (2019), 232–250  mathnet  crossref  crossref  adsnasa  isi  elib
    11. K. P. Isaev, “Predstavlyayuschie sistemy eksponent v prostranstvakh analiticheskikh funktsii”, Kompleksnyi analiz. Tselye funktsii i ikh primeneniya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 161, VINITI RAN, M., 2019, 3–64  mathnet
    12. K. P. Isaev, K. V. Trunov, R. S. Yulmukhametov, “Predstavlenie ryadami eksponent funktsii v normirovannykh podprostranstvakh $A^\infty (D)$”, Kompleksnyi analiz. Matematicheskaya fizika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 162, VINITI RAN, M., 2019, 42–56  mathnet
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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