Geodesic
Pseudodifferential Operators
Zbornik radova, Tome 7 (1997) no. 15, p. 111 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

The aim of lecture notes is to present the basic facts of the theory of pseudodifferential operators and to give sufficiently enough motivations for further study of this very important theory. Also, in the notes authors develop the theory of pseudodifferential operators within Colombeau's new generalized functions. Pseudo differential operators are generalization of differential operators. They form the minimal algebra of operators in which each elliptic operator has the inverse up to a smoothing operator. Thus, the roots of the theory of pseudodifferential operators are in the theory of elliptic operators. This theory is used for microlocal analysis of equations, the hypoellipticity for example. In the second part we show this for the (hypo )elliptic pseudodifferential equations with coefficients in the space of Colombeau's generalized functions. 
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     author = {M. Nedeljkov and D. Peri\v{s}i\'c and S. Pilipovi\'c},
     title = {Pseudodifferential {Operators}},
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M. Nedeljkov; D. Perišić; S. Pilipović. Pseudodifferential Operators. Zbornik radova, Tome 7 (1997) no. 15, p. 111 . http://geodesic.mathdoc.fr/item/ZR_1997_7_15_a3/