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The question of solvability

Dencker, Nils LU (2003) Hyperbolic problems and related topics In Graduate Series in Analysis p.159-184
Abstract
We give a 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 two 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
pseudodifferential operators, Nirenberg-Treves conjecture, solvability, principal type
in
Graduate Series in Analysis
editor
Colombini, Ferruccio and Nishitani, Tatsuo
pages
26 pages
publisher
International Press, Somerville, MA, USA
conference name
Hyperbolic problems and related topics
ISBN
1-57146-150-7
language
English
LU publication?
yes
id
a19f5fb2-c3f7-461d-b11d-f992cf79c11f (old id 795053)
date added to LUP
2007-12-27 17:05:06
date last changed
2017-02-08 14:45:53
@inproceedings{a19f5fb2-c3f7-461d-b11d-f992cf79c11f,
  abstract     = {We give a 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 two derivatives (compared with the elliptic case).},
  author       = {Dencker, Nils},
  booktitle    = {Graduate Series in Analysis},
  editor       = {Colombini, Ferruccio and Nishitani, Tatsuo},
  isbn         = {1-57146-150-7},
  keyword      = {pseudodifferential operators,Nirenberg-Treves conjecture,solvability,principal type},
  language     = {eng},
  pages        = {159--184},
  publisher    = {International Press, Somerville, MA, USA},
  title        = {The question of solvability},
  year         = {2003},
}