Loading [MathJax]/jax/element/mml/optable/GeneralPunctuation.js
Matematicheskie Zametki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



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






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


Matematicheskie Zametki, 1969, Volume 6, Issue 1, Pages 65–72 (Mi mzm6898)  

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

Self-adjoint abstract differential operators

M. M. Gekhtman

M. V. Lomonosov Moscow State University
Full-text PDF (497 kB) Citations (4)
Abstract: Let H be an abstract separable Hilbert space. We will consider the Hilbert space H1 whose elements are functions f(x) with domain H and we will also consider the set of self-adjoint operators Q(x) in H of the form Q(x)=A+B(x). In this formula AE, B(x)0, and the operator B(x) is bounded for all x. An operator L0 is defined on the set of finite, infinitely differentiable (in the strong sense) functions y(x)\inH1 according to the formula: L0y=y (-\infty<x<\infty). It is proved that the closure of the operator L_0 is a self-adjoint operator in H_1 under the given assumptions.
Received: 07.02.1968
English version:
Mathematical Notes, 1969, Volume 6, Issue 1, Pages 498–502
DOI: https://doi.org/10.1007/BF01450253
Bibliographic databases:
UDC: 513.88
Language: Russian
Citation: M. M. Gekhtman, “Self-adjoint abstract differential operators”, Mat. Zametki, 6:1 (1969), 65–72; Math. Notes, 6:1 (1969), 498–502
Citation in format AMSBIB
\Bibitem{Gek69}
\by M.~M.~Gekhtman
\paper Self-adjoint abstract differential operators
\jour Mat. Zametki
\yr 1969
\vol 6
\issue 1
\pages 65--72
\mathnet{http://mi.mathnet.ru/mzm6898}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=254667}
\zmath{https://zbmath.org/?q=an:0188.21002|0182.18404}
\transl
\jour Math. Notes
\yr 1969
\vol 6
\issue 1
\pages 498--502
\crossref{https://doi.org/10.1007/BF01450253}
Linking options:
  • https://www.mathnet.ru/eng/mzm6898
  • https://www.mathnet.ru/eng/mzm/v6/i1/p65
  • This publication is cited in the following 4 articles:
    1. V. I. Gorbachuk, M. L. Gorbachuk, “Some questions of the spectral theory of differential equations of elliptic type in the space of vector-functions”, Ukr Math J, 28:3 (1977), 244  crossref
    2. A. G. Brusentsev, F. S. Rofe-Beketov, “Selfadjointness conditions for strongly elliptic systems of arbitrary order”, Math. USSR-Sb., 24:1 (1974), 103–126  mathnet  crossref  mathscinet  zmath
    3. M. M. Gekhtman, “On the spectrum of an operator Sturm–Liouville equation”, Funct. Anal. Appl., 6:2 (1972), 151–152  mathnet  crossref  mathscinet  zmath
    4. L. I. Vainerman, M. L. Gorbachuk, “On self-adjoint semibounded abstract differential operators”, Ukr Math J, 22:6 (1971), 694  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
    Statistics & downloads:
    Abstract page:276
    Full-text PDF :103
    First page:1
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025