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Subordinacy analysis and absolutely continuous spectra for Sturm-Liouville equations with two singular endpoints

  Published:1998-03-01
 Printed: Mar 1998
  • Dominic P. Clemence
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Abstract

The Gilbert-Pearson characterization of the spectrum is established for a generalized Sturm-Liouville equation with two singular endpoints. It is also shown that strong absolute continuity for the one singular endpoint problem guarantees absolute continuity for the two singular endpoint problem. As a consequence, we obtain the result that strong nonsubordinacy, at one singular endpoint, of a particular solution guarantees the nonexistence of subordinate solutions at both singular endpoints.
MSC Classifications: 34L05, 34B20, 34B24 show english descriptions General spectral theory
Weyl theory and its generalizations
Sturm-Liouville theory [See also 34Lxx]
34L05 - General spectral theory
34B20 - Weyl theory and its generalizations
34B24 - Sturm-Liouville theory [See also 34Lxx]
 

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