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# Convolution Equation in $\mathcal{S}^{\prime\ast}$---Propagation of Singularities

Published:2001-03-01
Printed: Mar 2001
• Stevan Pilipović
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## Abstract

The singular spectrum of $u$ in a convolution equation $\mu * u = f$, where $\mu$ and $f$ are tempered ultradistributions of Beurling or Roumieau type is estimated by $$SS u \subset (\mathbf{R}^n \times \Char \mu) \cup SS f.$$ The same is done for $SS_{*}u$.
 MSC Classifications: 32A40 - Boundary behavior of holomorphic functions 46F15 - Hyperfunctions, analytic functionals [See also 32A25, 32A45, 32C35, 58J15] 58G07 - unknown classification 58G07