Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-16T17:04:37.206Z Has data issue: false hasContentIssue false

On the spectra of singular elliptic operators

Published online by Cambridge University Press:  26 February 2010

Martin Schechter
Affiliation:
Yeshiva University, New York, N.Y., U.S.A.
Get access

Abstract

We give sufficient conditions for the spectra and essential spectra of certain classes of operators to be contained in or coincide with an interval of the form [μ, ∞).

Type
Research Article
Copyright
Copyright © University College London 1976

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.)

References

1.Glazman, I. M.. Direct Methods of Qualitative Spectral Analysis of Singular Differential Operators, Israel Program of Scientific Translations (Jerusalem, 1965).Google Scholar
2.Naimark, M. A.. Linear Differential Operators, Part II (Frederich Ungar, New York, 1968).Google Scholar
3.Birman, M. S.. “The spectrum of singular boundary problems”, Mat. Sb., 55 (1961), 125174.Google Scholar
4.Miiller-Pfeiffer, E.. Spektraleigen-schaften eindimensionaler Differential-operatoren höherer Ordnung”, Studio Math., 34 (1970), 183196.Google Scholar
5.Miiller-Pfeiffer, E.. “Eine Bemerkung über das Spektrum des Schrödinger-Operators”, Math. Nach., 58 (1973), 299303.CrossRefGoogle Scholar
6.Schechter, Martin. Spectra of Partial Differential Operators (North Holland, Amsterdam, 1971).Google Scholar
7.Yafaev, D. R.. “On the spectrum of the perturbed polyharmonic operator”, Topics in Math. Phys., Vol. 5, Edited by Birman, M. S. (Plenum Press, New York, 1972, 107112).Google Scholar
8.Troesch, B. A.. “Integral inequalities for two functions”, Arch. Rat. Mech. Anal., 24 (1967), 128140.CrossRefGoogle Scholar
9.Mitrinović, D. S.. Analytic Inequalities (Springer, 1970).Google Scholar