RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb., 1992, Volume 183, Number 9, Pages 105–146 (Mi msb1074)  

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

On a class of unconditional bases in Hilbert spaces and on the problem of similarity of dissipative Volterra operators

G. M. Gubreev


Abstract: Let $B$ be a completely nonselfadjoint dissipative Volterra operator acting in a separable Hilbert space $\mathfrak Y$ whose resolvent $(I-\lambda B)^{-1}$ has finite exponential type. Further, let $\mathfrak{L}=(B-B^*)\mathfrak Y$, $y\in\mathfrak{L}$, and $y(\lambda)=(I-\lambda B)^{-1}y$. In this article conditions are determined on the operator $B$, the vector $y$, and the sequence $\Lambda=\{\lambda_k\}_{-\infty}^{+\infty}$ under which the family
$$ \{y(\lambda_k):\lambda_k\in \Lambda\}, \qquad \inf_{\lambda_k}\operatorname{Im}\lambda_k>0, $$
forms an unconditional basis in the space $\mathfrak Y$. Moreover, a new approach is considered for the problem of similarity of dissipative Volterra operators, based on a study of the basis properties of this system of vectors.

Full text: PDF file (3114 kB)
References: PDF file   HTML file

English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1994, 77:1, 93–126

Bibliographic databases:

UDC: 517.5
MSC: Primary 46B15, 47B44, 45D05; Secondary 30B50
Received: 09.07.1990

Citation: G. M. Gubreev, “On a class of unconditional bases in Hilbert spaces and on the problem of similarity of dissipative Volterra operators”, Mat. Sb., 183:9 (1992), 105–146; Russian Acad. Sci. Sb. Math., 77:1 (1994), 93–126

Citation in format AMSBIB
\Bibitem{Gub92}
\by G.~M.~Gubreev
\paper On a class of unconditional bases in Hilbert spaces and on the~problem of similarity of dissipative Volterra operators
\jour Mat. Sb.
\yr 1992
\vol 183
\issue 9
\pages 105--146
\mathnet{http://mi.mathnet.ru/msb1074}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1198837}
\zmath{https://zbmath.org/?q=an:0786.46015}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 77
\issue 1
\pages 93--126
\crossref{https://doi.org/10.1070/SM1994v077n01ABEH003431}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1994MZ10900007}


Linking options:
  • http://mi.mathnet.ru/eng/msb1074
  • http://mi.mathnet.ru/eng/msb/v183/i9/p105

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. G. M. Gubreev, “$L_2$-stable semigroups, Muckenhoupt weights, and unconditional bases of values of quasi-exponentials”, Sb. Math., 190:12 (1999), 1715–1747  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. G. M. Gubreev, “Unconditional Bases of Hilbert Spaces Composed of Values of Entire Vector Functions of Exponential Type”, Funct. Anal. Appl., 33:1 (1999), 52–55  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. I. Yu. Domanov, “Spectral Analysis of Powers of the Operator $(Vf)(x)=q(x)\int_0^xw(t)f(t)dt$”, Math. Notes, 73:3 (2003), 408–413  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Stevan Pilipović, Mirjana Stojanović, “Fractional differential equations through Laguerre expansions in abstract spaces: error estimates”, Integral Transforms and Special Functions, 17:12 (2006), 877  crossref
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:250
    Full text:77
    References:38
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019