Analytic continuation of fundamental solutions to differential equations with constant coefficients

Kiselman, Christer O.. "Analytic continuation of fundamental solutions to differential equations with constant coefficients." Annales de la faculté des sciences de Toulouse Mathématiques 20.S2 (2011): 153-182. <http://eudml.org/doc/219783>.

@article{Kiselman2011,
abstract = {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.},
affiliation = {Uppsala University, Department of Mathematics, P. O. Box 480, SE-751 06 Uppsala, Sweden.},
author = {Kiselman, Christer O.},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {fundamental solutions; differential equations; inverse Fourier transform},
language = {eng},
month = {4},
number = {S2},
pages = {153-182},
publisher = {Université Paul Sabatier, Toulouse},
title = {Analytic continuation of fundamental solutions to differential equations with constant coefficients},
url = {http://eudml.org/doc/219783},
volume = {20},
year = {2011},
}

TY - JOUR
AU - Kiselman, Christer O.
TI - Analytic continuation of fundamental solutions to differential equations with constant coefficients
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2011/4//
PB - Université Paul Sabatier, Toulouse
VL - 20
IS - S2
SP - 153
EP - 182
AB - 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.
LA - eng
KW - fundamental solutions; differential equations; inverse Fourier transform
UR - http://eudml.org/doc/219783
ER -