Norms of interpolational splines of odd degree in the spaces \(W_ 2^ k\) (Q920313)
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scientific article; zbMATH DE number 4163450
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Norms of interpolational splines of odd degree in the spaces \(W_ 2^ k\) |
scientific article; zbMATH DE number 4163450 |
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Norms of interpolational splines of odd degree in the spaces \(W_ 2^ k\) (English)
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1988
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Let \(W^ k_ 2\) be the Sobolev space of \(2\pi\)-periodic functions on the real line. The author shows that, in general, the norm of an interpolational polynomial spline of order 2k-1 viewed as an operator from \(W^ k_ 2\), is not equal to 1. He also constructs subspaces in \(W^ k_ 2\) such that the interpolation projections onto them have unit norms.
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Sobolev space
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interpolational polynomial spline
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interpolation projections
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