Hostname: page-component-7dd5485656-npwhs Total loading time: 0 Render date: 2025-10-31T00:31:42.015Z Has data issue: false hasContentIssue false
  • English
  • Français

The Friedrichs extension of regular ordinary differential operators

Published online by Cambridge University Press:  14 November 2011

Heinz-Dieter Niessen  and
Anton Zettl
Heinz-Dieter Niessen
Affiliation:
Department of Mathematics, University of Essen, Essen, Germany
Anton Zettl
Affiliation:
Department of Mathematics, University of Essen, Essen, Germany
Get access Rights & Permissions [Opens in a new window]

Synopsis

For regular symmetric ordinary differential expressions we show that (i) the minimal operator is bounded below and (ii) the Friedrichs extension is determined by Dirichlet boundary conditions. Both proofs are based on elementary inequalities.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 114 , Issue 3-4 , 1990 , pp. 229 - 236
Copyright
Copyright © Royal Society of Edinburgh 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1Dunford, N. and Schwartz, J. T.. Linear Operators, Vol II (New York:Interscience, 1963).Google Scholar
2Krein, M. G.. Theory of self-adjoint extensions of semi-bounded Hermitian operators and its applications, I, II. Mat. Sb. 20 (62) (1947), 431–495; Mat. Sb. 21 (63) (1947), 365–404.Google Scholar
3Kwong, M. K. and Zettl, A.. Weighted norm inequalities of sum form involving derivatives. Proc. Roy. Soc. Edinburgh Sect. A 88 (1981), 121–134.Google Scholar
4Naimark, M. A.. Linear Differential Operators, Vol II. (New York: Ungar, 1968).Google Scholar
5Weidmann, J.. Linear operators in Hilbert spaces. Graduate Texts inMathematics 68 (Berlin: Springer, 1980).Google Scholar
6Weidmann, J.. Spectral Theory of Ordinary Differential Operators. Lecture Notes in Mathematics 1258 (Berlin: Springer, 1987).CrossRefGoogle Scholar
7Zettl, A.. Formally self-adjoint quasi-differential operators. Rocky Mountain J. Math. 5 (1975), 4534–74.CrossRefGoogle Scholar