On ordinary differential operators of an odd degree non-similar to normal operators (Q2754836)
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scientific article; zbMATH DE number 1668456
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On ordinary differential operators of an odd degree non-similar to normal operators |
scientific article; zbMATH DE number 1668456 |
Statements
4 November 2001
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similar operators
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indefinite weight
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normal operator
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0.9064263
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0.89115775
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0.88228697
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0.8776014
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On ordinary differential operators of an odd degree non-similar to normal operators (English)
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The author considers the operator \(A=w^{-1}p(-i\frac{d}{dx})\) on \(L_2(\mathbb R)\), where \(p(z)\) is an odd degree polynomial with real coefficients, \(w\) is a real-valued step function taking a finite number of values. It is shown that if \(w(x)\) takes both positive and negative values, then \(A\) is not similar to a normal operator.
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