Asymptotic Methods in the Spectral Analysis of Sturm-Liouville Operators

Daphne Gilbert ()
Additional contact information
Daphne Gilbert: Dublin Institute of Technology, School of Mathematical Sciences

A chapter in Sturm-Liouville Theory, 2005, pp 121-136 from Springer

Abstract: Abstract We consider the relationship between the asymptotic behavior of solutions of the singular Sturm-Liouville equation and spectral properties of the corresponding self-adjoint operators. In particular, we review the main features of the theory of subordinacy by considering two standard cases, the half-line operator on L2([0, ∞)) and the full-line operator on L2(ℝ). It is assumed that the coefficient function q is locally integrable, that 0 is a regular endpoint in the half-line case, and that Weyl’s limit point case holds at the infinite endpoints. We note some consequences of the theory for the well-known informal characterization of the spectrum in terms of bounded solutions. We also consider extensions of the theory to related differential and difference operators, and discuss its application, in conjunction with other asymptotic methods, to some typical problems in spectral analysis.

Keywords: Minimal Support; Asymptotic Method; Essential Spectrum; Selfadjoint Operator; Stability Interval (search for similar items in EconPapers)
Date: 2005
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7643-7359-7_6

Ordering information: This item can be ordered from
http://www.springer.com/9783764373597

DOI: 10.1007/3-7643-7359-8_6

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().