Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The spectra of certain elliptic operators in $\textbf {R}^ N$

Author: Terence Brenner
Journal: Proc. Amer. Math. Soc. 103 (1988), 424-428
MSC: Primary 35P05; Secondary 35J30, 47F05
MathSciNet review: 943060
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give sufficient conditions for the spectra and essential spectra of certain classes of operators in ${R^N}$ to be contained in an interval of the form $[d,\infty )$.

References [Enhancements On Off] (What's this?)

  • M. Š. Birman, On the spectrum of singular boundary-value problems, Mat. Sb. (N.S.) 55 (97) (1961), 125–174 (Russian). MR 0142896
  • Terence Brenner, The spectra of the Schrodinger operators, Doctoral Dissertation, Yeshiva University, 1984.
  • I. M. Glazman, Direct methods of qualitative spectral analysis of singular differential operators, Israel Program for Scientific Translations, Jerusalem, 1965; Daniel Davey & Co., Inc., New York, 1966. Translated from the Russian by the IPST staff. MR 0190800
  • E. Müller-Pfeiffer, Spektraleigenschaften eindimensionaler Differentialoperatoren höherer Ordnung, Studia Math. 34 (1970), 183–196 (German). MR 265987, DOI
  • E. Müller-Pfeiffer, Eine Bemerkung über das Spektrum des Schrödinger-Operators, Math. Nachr. 58 (1973), 299–303 (German). MR 336110, DOI
  • M. A. Naĭmark, Lineĭ nye differentsial′nye operatory, Izdat. “Nauka”, Moscow, 1969 (Russian). Second edition, revised and augmented; With an appendix by V. È. Ljance. MR 0353061
  • Martin Schechter, Spectra of partial differential operators, 2nd ed., North-Holland Series in Applied Mathematics and Mechanics, vol. 14, North-Holland Publishing Co., Amsterdam, 1986. MR 869254
  • Martin Schechter, On the spectra of singular elliptic operators, Mathematika 23 (1976), no. 1, 107–115. MR 410115, DOI
  • D. R. Yafaev, On the spectrum of the perturbed polyharmonic operator, Topics in Math. Physics, Vol. 5 (M. S. Birman, ed.), Plenum Press, New York, 1972, pp. 107-112.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35P05, 35J30, 47F05

Retrieve articles in all journals with MSC: 35P05, 35J30, 47F05

Additional Information

Keywords: Spectrum of <IMG WIDTH="24" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$H$">, essential spectrum of <IMG WIDTH="24" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$H$">, selfadjoint
Article copyright: © Copyright 1988 American Mathematical Society