Self-adjoint differential operators of order are considered that are associated with the expression and the weighted Hilbert space . 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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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. 251–256DOI 10.4171/ZAA/150