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Sibirsk. Mat. Zh., 2015, Volume 56, Number 5, Pages 1130–1141 (Mi smj2702)  

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.

DOI: https://doi.org/10.17377/smzh.2015.56.512

Full text: PDF file (326 kB)
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English version:
Siberian Mathematical Journal, 2015, 56:5, 901–911

Bibliographic databases:

UDC: 517.951
Received: 23.12.2014

Citation: A. L. Pavlov, “On the division problem for a tempered distribution that depends holomorphically on a parameter”, Sibirsk. Mat. Zh., 56:5 (2015), 1130–1141; Siberian Math. J., 56:5 (2015), 901–911

Citation in format AMSBIB
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\by A.~L.~Pavlov
\paper On the division problem for a~tempered distribution that depends holomorphically on a~parameter
\jour Sibirsk. Mat. Zh.
\yr 2015
\vol 56
\issue 5
\pages 1130--1141
\mathnet{http://mi.mathnet.ru/smj2702}
\crossref{https://doi.org/10.17377/smzh.2015.56.512}
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\transl
\jour Siberian Math. J.
\yr 2015
\vol 56
\issue 5
\pages 901--911
\crossref{https://doi.org/10.1134/S0037446615050122}
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