Global hypoellipticity and continued fractions (Q810974)
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scientific article; zbMATH DE number 4215003
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Global hypoellipticity and continued fractions |
scientific article; zbMATH DE number 4215003 |
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Global hypoellipticity and continued fractions (English)
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1991
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The author considers a class of pseudodifferential operators on a d- dimensional torus like the Mathieu operator, \(-(\partial /\partial x_ 1)^ 2+2 \cos x_ 1.\) The main result is a characterization of global hypoellipticity of these operators in terms of continued fractions or Hill's determinant. As a consequence an asymptotic distribution of eigenvalues is obtained.
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pseudodifferential operator on torus
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global hypoellipticity
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0.8884883
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0.8882946
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0.8870758
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0.8862532
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0.8857085
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0.88565695
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0.8838465
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