Harmonic synthesis of solutions of elliptic equation with periodic coefficients (Q1313320)
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scientific article; zbMATH DE number 490692
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Harmonic synthesis of solutions of elliptic equation with periodic coefficients |
scientific article; zbMATH DE number 490692 |
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Harmonic synthesis of solutions of elliptic equation with periodic coefficients (English)
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6 April 1994
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An elliptic system in \(\mathbb{R}^ n\), which is invariant under the action of the group \(\mathbb{Z}^ n\) is considered. We construct a holomorphic family of finite-dimensional subrepresentations of the group in the space of solutions (Floquet solutions), such that any solution of the growth \(O\biggl( \exp \bigl( a | x | \bigr) \biggr)\) at infinity can be rewritten in the form of an integral over the family.
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representation of translation group
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coherent analytic sheaf
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Noether operator for a coherent sheaf
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approximation
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Floquet solutions
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Lasker- Noether decomposition
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elliptic system
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