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On subordinacy and analysis of the spectrum of one-dimensional Schrödinger operators. (English) Zbl 0666.34023

Authors’ summary: By considering the behaviour as \(N\to \infty\) of the ration of \(L_ 2[0,N]\) norms of solutions of \(-d^ 2u/dr^ 2+V(r)u=xu,\) \(0\leq r<\infty\), \(x\in {\mathbb{R}}\), a characterization of the absolutely continuous and singular spectra of one-dimensional Schrödinger operators is deduced. The analysis is applicable to all operators for which \(L=-d^ 2/dr^ 2+V(r)\) is regular at 0 and in the limit point case at infinity, with V(r) locally integrable.
Reviewer: B.D.Sleemann

MSC:

34L99 Ordinary differential operators
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