On Some Microlocal Properties of the Range of a Pseudo-Differential Operator of Principal Type
Abstract
The purpose of this paper is to obtain microlocal analogues of results by L. H örmander 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 $(\Psi)$.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2010
- DOI:
- 10.48550/arXiv.1003.1676
- arXiv:
- arXiv:1003.1676
- Bibcode:
- 2010arXiv1003.1676W
- Keywords:
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- Mathematics - Analysis of PDEs;
- 35S05 (Primary);
- 35A01;
- 58J40;
- 47G30 (Secondary)
- E-Print:
- With 1 figure. Corrected typos. Rewrote parts of Section 2 to account for new language. Corrected an erroneous comment following Theorem 2.19