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Zeitschrift für Analysis und ihre Anwendungen


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Volume 4, Issue 3, 1985, pp. 251–256
DOI: 10.4171/ZAA/150

Published online: 1985-06-30

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

Erich Müller-Pfeiffer[1] and St. Werler

(1) Pädagogische Hochschule, Erfurt, Germany

Self-adjoint differential operators of order $2n$ are considered that are associated with the expression $\mathcal A \equiv w^{-1} [(—1)^n (py^{(n)})^{(n)} + qy]$ and the weighted Hilbert space $L_{2, w}(0, \infty)$. 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.

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Müller-Pfeiffer Erich, Werler St.: A Necessary and Sufficient Discreteness Condition for the Spectrum of a two Term Differential Operator of Higher Order. Z. Anal. Anwend. 4 (1985), 251-256. doi: 10.4171/ZAA/150