The exponential calculus of microdifferential operators of infinite order. III
type: Item
instance of: scholarly article
title: The exponential calculus of microdifferential operators of infinite order. III
zbMATH Open document ID: 0535.35083
author: Takashi Aoki
published in: Proceedings of the Japan Academy. Series A
publication date: 1983-01-01T00:00:00Z
review text: The \(micro(=pseudo)\) differential operator defined by a symbol P(x,\(\xi)\) is denoted by :P(x,\(\xi)\):. A symbol p is said to be of order 1-0 if \(p(x,\xi)/| \xi | \to 0\) as \(| \xi | \to \infty\). Let p and q be symbols of order 1-0. Let a and b be symbols of order \(m_ 1\) and of order \(m_ 2\) respectively. In this paper, the author constructs symbols r and c of order 1-0 and of order \(m_ 1+m_ 2\) respectively satisfying \(:a\cdot\exp(p): :b\cdot\exp(q): = :c\cdot\exp(r):\). This gives a generalization of one of the main resuls of part I and II [cf., the author, Ann. Inst. Fourier 33, N. 4, 227-250 (1983; Zbl 0495.58025)].
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 58J15
zbMATH DE Number: 3849751
zbMATH Keywords: exponential calculus
zbMATH Keywords: microdifferential operators
zbMATH Keywords: infinite order
MaRDI profile type: Publication
full work available at URL: pjaa.59.79
OpenAlex ID: W4242541148
cites work: Invertibility of microdifferential operators of infinite order
cites work: The exponential calculus of microdifferential operators of infinite order. I, II
cites work: Calcul exponentiel des opérateurs microdifférentiel d'ordre infini. I
cites work: Fourier integral operators. I
cites work: Singular Cauchy problems for second order partial differential operators with non-involutory characteristics
DOI: 10.3792/PJAA.59.79
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description: scientific article; zbMATH DE number 3849751