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Zeitschrift für Analysis und ihre Anwendungen


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Volume 3, Issue 4, 1984, pp. 367–369
DOI: 10.4171/ZAA/114

Published online: 1984-08-31

A Remark on the Qualitative Spectral Theory or Sturm-Liouville Operators

Erich Müller-Pfeiffer[1]

(1) Pädagogische Hochschule, Erfurt, Germany

If $N (\Lambda)$ denotes the maximal number of zeros of the non-trivial solutions of the Sturm-Liouville equation $$—(p(x) u’)’ + q(x) u = \Lambda u, \quad -\infty \leq a < x < b \leq \infty,$$ then under some hypothesis the number of eigenvalues of a special selfadjoint operator (Friedrichs extension) is equal to $N\Lambda - 1$ below $\Lambda$.

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Müller-Pfeiffer Erich: A Remark on the Qualitative Spectral Theory or Sturm-Liouville Operators. Z. Anal. Anwend. 3 (1984), 367-369. doi: 10.4171/ZAA/114