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Generators for rings of compactly supported distributions
Stockholm University, Faculty of Science, Department of Mathematics.
2011 (English)In: Integral equations and operator theory, ISSN 0378-620X, E-ISSN 1420-8989, Vol. 69, no 1, 63-71 p.Article in journal (Refereed) Published
Abstract [en]

Let CUnknown control sequence '\tt' denote a closed convex cone in \mathbb RdRd with apex at 0. We denote by E¢(C)Unknown control sequence '\tt' the set of distributions on \mathbb RdRd having compact support contained in CUnknown control sequence '\tt'. Then E¢(C)Unknown control sequence '\tt' is a ring with the usual addition and with convolution. We give a necessary and sufficient analytic condition on [^(f)]1,..., [^(f)]nf1fn for f1,... ,fn Î E¢(C)Unknown control sequence '\tt' to generate the ring E¢(C)Unknown control sequence '\tt'. (Here [^(  ·  )] denotes Fourier-Laplace transformation.) This result is an application of a general result on rings of analytic functions of several variables by Lars Hörmander. En route we answer an open question posed by Yutaka Yamamoto.

Place, publisher, year, edition, pages
2011. Vol. 69, no 1, 63-71 p.
Keyword [en]
Rings of distributions, compactly supported distributions, Fourier-Laplace transform, corona type problem.
National Category
Mathematical Analysis
Research subject
URN: urn:nbn:se:su:diva-51617DOI: 10.1007/s00020-010-1842-3ISI: 000286526300003OAI: diva2:385371
Available from: 2011-01-11 Created: 2011-01-11 Last updated: 2012-01-23Bibliographically approved

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Maad Sasane, Sara
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