On the negative squares of indefinite Sturm--Liouville operators (Q996968)
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scientific article; zbMATH DE number 5173086
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the negative squares of indefinite Sturm--Liouville operators |
scientific article; zbMATH DE number 5173086 |
Statements
On the negative squares of indefinite Sturm--Liouville operators (English)
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19 July 2007
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Sturm--Liouville operators on the half-line \(x>0\) are studied. The number of negative squares of all self-adjoint extensions of a simple symmetric operator of defect one with finitely many negative squares is characterized in terms of the behaviour of an abstract Titchmarsh--Weyl function near \(0\) and \(\infty\). The results are applied to a class of symmetric and selfadjoint indefinite Sturm--Liouville operators with indefinite weight functions.
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Sturm-Liouville differential operators
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Kreĭn spaces
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Weyl functions
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operators with finitely many negative squares
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definitizable operators
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symmetric and selfadjoint operators
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boundary triplets
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generalised Nevanlinna functions
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definitisable functions
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