Analytic extension of Beurling's ultradistributions of \(L_2\)-growth by Cauchy integrals (Q2796449)
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scientific article; zbMATH DE number 6560218
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Analytic extension of Beurling's ultradistributions of \(L_2\)-growth by Cauchy integrals |
scientific article; zbMATH DE number 6560218 |
Statements
24 March 2016
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Beurling's ultradistribution
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strongly elliptic
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Cauchy integral
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analytic extension
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Analytic extension of Beurling's ultradistributions of \(L_2\)-growth by Cauchy integrals (English)
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Let \(C\) be an open convex cone in \({\mathbb R}^n\) and let \(U\in {\mathcal D}'_{L_2, (\omega)}({\mathbb R}^N)\) be an ultradistribution of Beurling type and \(L_2\)-growth. The author gives a sufficient condition under which the Cauchy integral \(C(U, x+iy)\) of \(U\) corresponding to \(C\) does have \(U\) as boundary values when \(y\to 0,\) \(y\in C.\)
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