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

We give sufficient conditions ensuring a construction of solution to the equation with σ ∈ ℝ n and λ ∈ G ⊂ ℂ, where f ( λ ) and u ( λ ) are tempered distributions depending holomorphically on λ , while the polynomial P m ( σ ) may have real zeros.

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Published in:Siberian mathematical journal 2015-09, Vol.56 (5), p.901-911
Main Author: Pavlov, A. L.
Format: Article
Language:English
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Mathematics
Mathematics and Statistics
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description We give sufficient conditions ensuring a construction of solution to the equation with σ ∈ ℝ n and λ ∈ G ⊂ ℂ, where f ( λ ) and u ( λ ) are tempered distributions depending holomorphically on λ , while the polynomial P m ( σ ) may have real zeros.
doi_str_mv 10.1134/S0037446615050122
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subjects Mathematics
Mathematics and Statistics
title On the division problem for a tempered distribution that depends holomorphically on a parameter
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