JournalszaaVol. 3, No. 4pp. 367–369

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

  • Erich Müller-Pfeiffer

    Pädagogische Hochschule, Erfurt, Germany
A Remark on the Qualitative Spectral Theory or Sturm-Liouville Operators cover
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Abstract

If N(Λ)N (\Lambda) denotes the maximal number of zeros of the non-trivial solutions of the Sturm-Liouville equation

—(p(x)u’)’+q(x)u=Λu,−∞≤a<x<b≤∞,—(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 NΛ−1N\Lambda - 1 below Λ\Lambda.

Cite this article

Erich Müller-Pfeiffer, A Remark on the Qualitative Spectral Theory or Sturm-Liouville Operators. Z. Anal. Anwend. 3 (1984), no. 4, pp. 367–369

DOI 10.4171/ZAA/114