Some remarks on convolution equations

C. A. Berenstein; M. A. Dostal

Annales de l'institut Fourier (1973)

  • Volume: 23, Issue: 1, page 55-73
  • ISSN: 0373-0956

Abstract

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Using a description of the topology of the spaces E ' ( Ω ) ( Ω open convex subset of R n ) via the Fourier transform, namely their analytically uniform structures, we arrive at a formula describing the convex hull of the singular support of a distribution T , T ∈ E ' . We give applications to a class of distributions T satisfying cv. sing. supp. S * T = cv. sing. supp. S + cv. sing. supp. T for all S ∈ E ' .

How to cite

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Berenstein, C. A., and Dostal, M. A.. "Some remarks on convolution equations." Annales de l'institut Fourier 23.1 (1973): 55-73. <http://eudml.org/doc/74113>.

@article{Berenstein1973,
abstract = {Using a description of the topology of the spaces $\{\bf E\}^\{\prime \}(\Omega )$ ($\Omega $ open convex subset of $R^n$) via the Fourier transform, namely their analytically uniform structures, we arrive at a formula describing the convex hull of the singular support of a distribution $T$, $T\in \{\bf E\}^\{\prime \}$. We give applications to a class of distributions $T$ satisfying\begin\{\}\text\{cv.\} \text\{sing.\} \text\{supp.\}\, S*T=\, \text\{cv.\} \text\{sing.\} \text\{supp.\}\, S+ \,\text\{cv.\} \text\{sing.\} \text\{supp.\}\, T\end\{\}for all $S\in \{\bf E\}^\{\prime \}$.},
author = {Berenstein, C. A., Dostal, M. A.},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {1},
pages = {55-73},
publisher = {Association des Annales de l'Institut Fourier},
title = {Some remarks on convolution equations},
url = {http://eudml.org/doc/74113},
volume = {23},
year = {1973},
}

TY - JOUR
AU - Berenstein, C. A.
AU - Dostal, M. A.
TI - Some remarks on convolution equations
JO - Annales de l'institut Fourier
PY - 1973
PB - Association des Annales de l'Institut Fourier
VL - 23
IS - 1
SP - 55
EP - 73
AB - Using a description of the topology of the spaces ${\bf E}^{\prime }(\Omega )$ ($\Omega $ open convex subset of $R^n$) via the Fourier transform, namely their analytically uniform structures, we arrive at a formula describing the convex hull of the singular support of a distribution $T$, $T\in {\bf E}^{\prime }$. We give applications to a class of distributions $T$ satisfying\begin{}\text{cv.} \text{sing.} \text{supp.}\, S*T=\, \text{cv.} \text{sing.} \text{supp.}\, S+ \,\text{cv.} \text{sing.} \text{supp.}\, T\end{}for all $S\in {\bf E}^{\prime }$.
LA - eng
UR - http://eudml.org/doc/74113
ER -

References

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  15. [15] B. MALGRANGE, Sur la propagation de la régularité des solutions des équations à coefficients constants, Bull. Math. Soc. Sci. Math. Phys. R.P. Roumaine, 3 (1959), 432-440. Zbl0109.32002
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