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Generators for Rings of Compactly Supported Distributions
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
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 C denote a closed convex cone in R-d with apex at 0. We denote by E'(C) the set of distributions on R-d having compact support contained in C. Then E'(C) is a ring with the usual addition and with convolution. We give a necessary and sufficient analytic condition on (f) over cap (1), ..., (f) over cap (n) for f(n) is an element of E'(C) to generate the ring E'(C). (Here (center dot) over cap denotes Fourier-Laplace transformation.) This result is an application of a general result on rings of analytic functions of several variables by Lars Hormander. 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
Computational Mathematics
URN: urn:nbn:se:kth:diva-30544DOI: 10.1007/s00020-010-1842-3ISI: 000286526300003ScopusID: 2-s2.0-84904982711OAI: diva2:401637
QC 20110303Available from: 2011-03-03 Created: 2011-02-28 Last updated: 2011-03-03Bibliographically approved

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Sasane, Sara MaadSasane, Amol
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