This article is cited in 2 papers

On the division problem for a tempered distribution that depends holomorphically on a parameter

A. L. Pavlov

Donetsk National University, Donetsk, Ukraine

Abstract: We give sufficient conditions ensuring a construction of solution to the equation
$$ \sum^m_{k=0}P_k(\sigma)\lambda^ku(\lambda)=f(\lambda), $$
with $\sigma\in\mathbb R^n$ and $\lambda\in G\subset\mathbb C$, where $f(\lambda) and u(\lambda)$are tempered distributions depending holomorphically on $\lambda$, while the polynomial $P_m(\sigma)$ may have real zeros.

Keywords: tempered distribution, regularization, Petrovskiĭ correct polynomial.

UDC: 517.951

Received: 23.12.2014

DOI: 10.17377/smzh.2015.56.512

 English version: Siberian Mathematical Journal, 2015, 56:5, 901–911

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