On Gröchenig, Heil, and Walnut's proof of the local three squares theorem (Q1810337)
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scientific article; zbMATH DE number 1928892
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Gröchenig, Heil, and Walnut's proof of the local three squares theorem |
scientific article; zbMATH DE number 1928892 |
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On Gröchenig, Heil, and Walnut's proof of the local three squares theorem (English)
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16 June 2003
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The main result says the following. Consider strictly positive numbers \(r_2> r_1\) for which \(r_1/r_2 \notin Q\), and let \(\mu_k\) denote the characteristic function for the interval \([-r_k,r_k]\). Then the set of functions of the form \((g_1 \mu_1)*\mu_2+ \mu_1*(g_2\mu_2)\) with \(g_1,g_2\in L^2(-(r_1+r_2),r_1+r_2)\) is dense in \(L^2(-(r_1+r_2),r_1+r_2)\). A \(d\)-dimensional version is obtained by convolution.
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completeness
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locl three squares theorem
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