On Some Microlocal Properties of the Range of a Pseudo-Differential Operator of Principal Type

Jens Wittsten

doi:10.2140/apde.2012.5.423

On Some Microlocal Properties of the Range of a Pseudo-Differential Operator of Principal Type

Analysis of PDEs 2015-02-13 v4

Authors: Jens Wittsten

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Abstract

The purpose of this paper is to obtain microlocal analogues of results by L. H \"ormander about inclusion relations between the ranges of first order differential operators with coefficients in $C^\infty$ which fail to be locally solvable. Using similar techniques, we shall study the properties of the range of classical pseudo-differential operators of principal type which fail to satisfy condition $(\Psi)$ .

Keywords

microlocal analysis pseudo-differential operator principal type range properties local solvability condition (psi)

Cite

@article{arxiv.1003.1676,
  title  = {On Some Microlocal Properties of the Range of a Pseudo-Differential Operator of Principal Type},
  author = {Jens Wittsten},
  journal= {arXiv preprint arXiv:1003.1676},
  year   = {2015}
}

Comments

With 1 figure. Corrected typos. Rewrote parts of Section 2 to account for new language. Corrected an erroneous comment following Theorem 2.19

On Some Microlocal Properties of the Range of a Pseudo-Differential Operator of Principal Type

Abstract

Keywords

Cite

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