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Operators that coerce the surjectivity of convolution
Mälardalen University, School of Education, Culture and Communication. (Mathematics/Applied Mathematics)
2013 (English)Report (Other academic)
Abstract [en]

Considered are operators that leave the set of non-invertible (in the sense of Ehrenpreis) distributions stable. They simultaneously generalise the operation of convolution by a distribution with compact support and the operation of multiplication by a real analytic function; they are here called pseudo-convolutions since they also generalise pseudo-differential operators. (It is shown that the elliptic real analytic pseudo-differential operators leave both the non-invertible and the invertible distributions invariant.) But when the condition of real-analyticity is relaxed, such operators may map a non-invertible distribution to one invertible -- given that the invertibility in both cases concerns the same function space. By varying the space, however, one can measure the 'loss of non-invertibily' that a non-analytic perturbation may introduce. This phenomenon is here studied using the Beurling classes of functions and measuring the regularity of operator symbols in the Denjoy-Carleman sense; the Gevrey case turns out particularly simple.

Place, publisher, year, edition, pages
2013.
National Category
Other Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-24074OAI: oai:DiVA.org:mdh-24074DiVA: diva2:682912
Available from: 2013-12-30 Created: 2013-12-30 Last updated: 2014-01-07Bibliographically approved

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Other links

http://arxiv.org/abs/1312.4772

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