Pseudodifferential Operators
Zbornik radova, Tome 7 (1997) no. 15, p. 111
Cet article a éte moissonné depuis 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.
@article{ZR_1997_7_15_a3,
author = {M. Nedeljkov and D. Peri\v{s}i\'c and S. Pilipovi\'c},
title = {Pseudodifferential {Operators}},
journal = {Zbornik radova},
pages = {111 },
year = {1997},
volume = {7},
number = {15},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ZR_1997_7_15_a3/}
}
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/