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Mat. Sb., 1999, Volume 190, Number 12, Pages 3–36 (Mi msb442)  

This article is cited in 4 scientific papers (total in 4 papers)

$L_2$-stable semigroups, Muckenhoupt weights, and unconditional bases of values of quasi-exponentials

G. M. Gubreev

South Ukrainian State K. D. Ushynsky Pedagogical University

Abstract: A class of unbounded operators with discrete spectrum in a separable Hilbert space is distinguished, in which the property of being the generator of an $L_2$-stable semigroup is equivalent to the similarity to the Sz.-Nadya–Foiash scalar model. In the proof of this result a connection with the theory of Muckenhoupt weights is established. A criterion for the similarity of a dissipative unicellular operator to the simplest integration operator is also derived. The notion of a quasiexponential, an abstract analogue of an exponential, is introduced. As an application, a description of all unconditional bases in the Hilbert space consisting of values of a quasiexponential is presented.

DOI: https://doi.org/10.4213/sm442

Full text: PDF file (414 kB)
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English version:
Sbornik: Mathematics, 1999, 190:12, 1715–1747

Bibliographic databases:

UDC: 517.986+517.444+517.5
MSC: Primary 47B99, 47B44, 47G10; Secondary 46C10, 42A50
Received: 01.02.1999

Citation: G. M. Gubreev, “$L_2$-stable semigroups, Muckenhoupt weights, and unconditional bases of values of quasi-exponentials”, Mat. Sb., 190:12 (1999), 3–36; Sb. Math., 190:12 (1999), 1715–1747

Citation in format AMSBIB
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\jour Mat. Sb.
\yr 1999
\vol 190
\issue 12
\pages 3--36
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\transl
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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. G. M. Gubreev, “The Structure of Model Volterra Operators, Biorthogonal Expansions, and Interpolation in Regular de Branges Spaces”, Funct. Anal. Appl., 35:2 (2001), 142–145  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. G. M. Gubreev, “Regular Mittag-Leffler Kernels and Volterra Operators”, Funct. Anal. Appl., 38:4 (2004), 305–308  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. G. M. Gubreev, “Regular Mittag-Leffler kernels and spectral decomposition of a class of non-selfadjoint operators”, Izv. Math., 69:1 (2005), 15–57  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. Gubreev G., Tarasenko A., “On the Theory of Unconditional Bases of Hilbert Spaces Formed By Entire Vector-Functions”, Bol. Soc. Mat. Mex., 24:1 (2018), 269–278  crossref  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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