JournalszaaVol. 4, No. 3pp. 251–256

A Necessary and Sufficient Discreteness Condition for the Spectrum of a two Term Differential Operator of Higher Order

  • Erich Müller-Pfeiffer

    Pädagogische Hochschule, Erfurt, Germany
  • St. Werler

    Pädagogische Hochschule, Erfurt, Germany
A Necessary and Sufficient Discreteness Condition for the Spectrum of a two Term Differential Operator of Higher Order cover
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Abstract

Self-adjoint differential operators of order 2n2n are considered that are associated with the expression Aw1[(1)n(py(n))(n)+qy]\mathcal A \equiv w^{-1} [(—1)^n (py^{(n)})^{(n)} + qy] and the weighted Hilbert space L2,w(0,)L_{2, w}(0, \infty). By use of discreteness conditions for the spectrum of such operators given by Kwong and Zettl a necessary and sufficient condition for the discreteness of the spectrum is established.

Cite this article

Erich Müller-Pfeiffer, St. Werler, A Necessary and Sufficient Discreteness Condition for the Spectrum of a two Term Differential Operator of Higher Order. Z. Anal. Anwend. 4 (1985), no. 3, pp. 251–256

DOI 10.4171/ZAA/150