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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
Mathematics
##### Identifiers
ISI: 000286526300003OAI: oai:DiVA.org:su-51617DiVA: diva2:385371
Available from: 2011-01-11 Created: 2011-01-11 Last updated: 2012-01-23Bibliographically approved

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