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The solvability of pseudo-differential operators

Dencker, Nils LU (2004) Phase space analysis of partial differential equations In [Host publication title missing] 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).
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Nirenberg-Treves conjecture, pseudodifferential operators, principal type, solvability
in
[Host publication title missing]
editor
Colombini, Ferruccio; Pernazza, Ludovico; and
volume
1
pages
26 pages
publisher
Pubbl. Cent. Ric. Mat. Ennio Giorgi
conference name
Phase space analysis of partial differential equations
ISBN
88-7642-150-5
language
English
LU publication?
yes
id
f97f7152-010f-46bc-bd15-10d6138d912d (old id 795037)
date added to LUP
2007-12-27 17:01:35
date last changed
2017-02-08 14:45:53
@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},
  keyword      = {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},
}