Solvability of Lewy equation in the space of the tempered ultrahyperfunctions
type: Item
instance of: scholarly article
title: Solvability of Lewy equation in the space of the tempered ultrahyperfunctions
zbMATH Open document ID: 1266.46027
author: Yasuyuki Oka
author: Kunio Yoshino
published in: Journal of Pseudo-Differential Operators and Applications
publication date: 2013-03-25T00:00:00Z
review text: It is shown that the Lewy equation has a solution in spaces of tempered ultrahyperfunctions which are smaller than the space of the Fourier ultrahyperfunctions \({\mathcal G}'(\mathbb{R})\) (see [\textit{S.-Y. Chung, D. Kim} and \textit{S. K. Kim}, J. Fac. Sci., Univ. Tokyo, Sect. I A, 40, No. 1, 63--71 (1993; Zbl 0796.46027)]). In particular, it is demonstrated that the Lewy equation for a source function \(f \in C_0^1 (\mathbb{R}_{x,y}^2; L^1(\mathbb{R}_t))\) has a solution in the space \(C^1 (\mathbb{R}_{x,y}^2; (\tilde{S}^1)^{\prime})(\mathbb{R}_t),\) where the space \((\tilde{S}^1)^{\prime}(\mathbb{R})\) is the space of tempered ultrahyperfunctions.
Mathematics Subject Classification ID: 46F05
Mathematics Subject Classification ID: 46F15
Mathematics Subject Classification ID: 35A01
zbMATH DE Number: 6148492
zbMATH Keywords: Sobolev-Schwartz theory
zbMATH Keywords: Gel'fand-Shilov space
zbMATH Keywords: tempered ultrahyperfunctions
zbMATH Keywords: Lewy equation
zbMATH Keywords: distributions
Wikidata QID: Q115377588
reviewed by: Denis Sidorov
MaRDI profile type: Publication
full work available at URL: s11868-012-0052-y
OpenAlex ID: W1984930818
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DOI: 10.1007/S11868-012-0052-Y
description: scientific article; zbMATH DE number 6148492