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The solvability of pseudo-differential operators

Dencker, Nils LU (2004) Phase space analysis of partial differential equations 1. p.175-200
Abstract
We give a new proof of the Nirenberg-Treves conjecture: that local solvability of principal type pseudodifferential operators is equivalent to condition (Psi). This condition rules out sign changes from - to + of the imaginary part of the principal symbol along the oriented bicharacteristics of the real part. We obtain local solvability by proving a localizable a priori estimate for the adjoint operator with a loss of arbitrary more than 3/2 derivatives (compared with the elliptic case).
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Nirenberg-Treves conjecture, pseudodifferential operators, principal type, solvability
host publication
[Host publication title missing]
editor
Colombini, Ferruccio and Pernazza, Ludovico
volume
1
pages
26 pages
publisher
Pubbl. Cent. Ric. Mat. Ennio Giorgi
conference name
Phase space analysis of partial differential equations
conference dates
0001-01-02
ISBN
88-7642-150-5
language
English
LU publication?
yes
id
f97f7152-010f-46bc-bd15-10d6138d912d (old id 795037)
date added to LUP
2016-04-04 11:32:46
date last changed
2018-11-21 21:05:33
@inproceedings{f97f7152-010f-46bc-bd15-10d6138d912d,
  abstract     = {{We give a new proof of the Nirenberg-Treves conjecture: that local solvability of principal type pseudodifferential operators is equivalent to condition (Psi). This condition rules out sign changes from - to + of the imaginary part of the principal symbol along the oriented bicharacteristics of the real part. We obtain local solvability by proving a localizable a priori estimate for the adjoint operator with a loss of arbitrary more than 3/2 derivatives (compared with the elliptic case).}},
  author       = {{Dencker, Nils}},
  booktitle    = {{[Host publication title missing]}},
  editor       = {{Colombini, Ferruccio and Pernazza, Ludovico}},
  isbn         = {{88-7642-150-5}},
  keywords     = {{Nirenberg-Treves conjecture; pseudodifferential operators; principal type; solvability}},
  language     = {{eng}},
  pages        = {{175--200}},
  publisher    = {{Pubbl. Cent. Ric. Mat. Ennio Giorgi}},
  title        = {{The solvability of pseudo-differential operators}},
  volume       = {{1}},
  year         = {{2004}},
}