Propagation of singularities for operators with multiple involutive characteristics

Sjöstrand, Johannes. "Propagation of singularities for operators with multiple involutive characteristics." Annales de l'institut Fourier 26.1 (1976): 141-155. <http://eudml.org/doc/74263>.

@article{Sjöstrand1976,
abstract = {Let $P$ be a classical pseudodifferential operator of order $m$ on a paracompact $C^\infty $ manifold $X$. Let $p_m$ be the principal symbol and assume that $\Sigma =p^\{-1\}_m(0)$ is an involutive $C^\infty $ sub-manifold of $T^*X\setminus 0$, satisfying a certain transversality condition. We assume that $p_m$ vanishes exactly to order $M$ on $\Sigma $ and that the derivatives of order $M$ satisfy a certain condition, inspired from the Calderòn uniqueness theorem (usually empty when $M=2$). Suppose that a Levi condition is valid for the lower order symbols. If $u\in \{\cal D\}^\{\prime \}(X)$, $Pu\in C^\infty (X)$, then $WF(u)$ is a union of (bicharacteristic leaves), defined in the paper).},
author = {Sjöstrand, Johannes},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {1},
pages = {141-155},
publisher = {Association des Annales de l'Institut Fourier},
title = {Propagation of singularities for operators with multiple involutive characteristics},
url = {http://eudml.org/doc/74263},
volume = {26},
year = {1976},
}

TY - JOUR
AU - Sjöstrand, Johannes
TI - Propagation of singularities for operators with multiple involutive characteristics
JO - Annales de l'institut Fourier
PY - 1976
PB - Association des Annales de l'Institut Fourier
VL - 26
IS - 1
SP - 141
EP - 155
AB - Let $P$ be a classical pseudodifferential operator of order $m$ on a paracompact $C^\infty $ manifold $X$. Let $p_m$ be the principal symbol and assume that $\Sigma =p^{-1}_m(0)$ is an involutive $C^\infty $ sub-manifold of $T^*X\setminus 0$, satisfying a certain transversality condition. We assume that $p_m$ vanishes exactly to order $M$ on $\Sigma $ and that the derivatives of order $M$ satisfy a certain condition, inspired from the Calderòn uniqueness theorem (usually empty when $M=2$). Suppose that a Levi condition is valid for the lower order symbols. If $u\in {\cal D}^{\prime }(X)$, $Pu\in C^\infty (X)$, then $WF(u)$ is a union of (bicharacteristic leaves), defined in the paper).
LA - eng
UR - http://eudml.org/doc/74263
ER -