There are no unconditional Schauder frames of translates in \(L^p(\mathbb{R})\), \(1 \leqslant p \leqslant 2\) (Q6662437)
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scientific article; zbMATH DE number 7966468
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | There are no unconditional Schauder frames of translates in \(L^p(\mathbb{R})\), \(1 \leqslant p \leqslant 2\) |
scientific article; zbMATH DE number 7966468 |
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There are no unconditional Schauder frames of translates in \(L^p(\mathbb{R})\), \(1 \leqslant p \leqslant 2\) (English)
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14 January 2025
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The authors solve an open problem in frame theory, i.e., do there exist unconditional Schauder frames of translates in \(L^p(\mathbb R)\) for \(1\leq p\leq 2\)? They give a negative answer, and they prove it by contradiction using smart techniques.\N\NIt has been known previously that the answer is positive for $p>2$ [\textit{D.~Freeman} et al., Isr. J. Math. 203, 189--209 (2014; Zbl 1305.42033)].
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Schauder frame
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translates
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