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Zbl 0675.35091
Bourdaud, Gérard
Une algèbre maximale d'opérateurs pseudo-différentiels de type 1,1. (A maximal algebra of pseudodifferential operators of type 1,1). (French)
[J] Sémin., Équations Dériv. Partielles 1987-1988, Exp. No.7, 17 p. (1988).

This seminar is devoted to $opS\sp 0\sb{1,1}$, the class of all the pseudo-differential operators with symbol in $S\sp 0\sb{1,1}$; it summarizes results obtained previously by the author, Hörmander and other authors, concerning the algebra of all $L\sp 2$-bounded operators in $opS\sp 0\sb{1,1}$ (operators in $opS\sp 0\sb{1,1}$ are not $L\sp 2$- bounded in general). A new presentation of these results is given in the seminar, by arguing on kernels and first characterizing operators in $opS\sp 0\sb{1,1}$ through their action on suitable classes of test functions.
[L.Rodino]

MSC 2000:: *35S05 General theory of pseudodifferential operators

Keywords: survey; algebra of all $L\sp 2$-bounded operators; kernels; characterizing operators; classes of test functions

Cited in: Zbl 0763.35114

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