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Analytic continuation of fundamental solutions to differential equations with constant coefficients
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2011 (English)In: Annales de la Faculté des Sciences de Toulouse, Mathématiques, ISSN 0240-2963, Vol. (6) 20, no S2, 153-182 p.Article in journal (Refereed) Published
Abstract [en]

If $P$ is a polynomial in ${\bf R}^n$ such that $1/P$ integrable, then the inverse Fourier transform of $1/P$ is a fundamental solution $E_P$ to the differential operator $P(D)$. The purpose of the article is to study the dependence of this fundamental solution on the polynomial $P$. For $n=1$ it is shown that $E_P$ can be analytically continued to a Riemann space over the set of all polynomials of the same degree as $P$. The singularities of this extension are studied.

Place, publisher, year, edition, pages
Toulouse: Université Paul Sabatier , 2011. Vol. (6) 20, no S2, 153-182 p.
Keyword [en]
Partial differenatial equations
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-171622OAI: oai:DiVA.org:uu-171622DiVA: diva2:511905
Available from: 2012-03-23 Created: 2012-03-23 Last updated: 2014-12-09

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http://www.numdam.org/item?id=AFST_2011_6_20_S2_153_0http://www.cb.uu.se/~kiselman

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Kiselman, Christer O.

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