The authors consider classical analytic pseudodifferential operators of the form $P(t,x,D_t,D_x)=(tD_t)^m+Q_{m-1}(t,x,D_t,D_x)$. The arguments are microlocal, near a point $z_0=(0,x_0;0,\xi_0)$ of the symplectic characteristic manifold $\{t=0, \tau=0\}$, generalizing results by A. Bove, J. E. Lewis and C. Parenti \ref[ Propagation of singularities for Fuchsian operators, Lecture Notes in Math., 984, Springer, Berlin, 1983; and, in the case $m=1$, previous contributions by Hanges, Ivrii, and Melrose. With respect to the papers of the above-mentioned authors, here no Levi condition is needed on the lower order terms $Q_{m-1}$, the result being stated in terms of Gevrey classes $G^s$ with $1\leq s<m/(m-1)$ (if $m=1$ then $1\leq s\leq\infty$). In particular, propagation of singularities is proved along the half-bicharacteristics emanating from $z_0$.
Propagation of analytic and Gevrey singularities for operators with noninvolutive characteristics.
ZANGHIRATI, Luisa
1993
Abstract
The authors consider classical analytic pseudodifferential operators of the form $P(t,x,D_t,D_x)=(tD_t)^m+Q_{m-1}(t,x,D_t,D_x)$. The arguments are microlocal, near a point $z_0=(0,x_0;0,\xi_0)$ of the symplectic characteristic manifold $\{t=0, \tau=0\}$, generalizing results by A. Bove, J. E. Lewis and C. Parenti \ref[ Propagation of singularities for Fuchsian operators, Lecture Notes in Math., 984, Springer, Berlin, 1983; and, in the case $m=1$, previous contributions by Hanges, Ivrii, and Melrose. With respect to the papers of the above-mentioned authors, here no Levi condition is needed on the lower order terms $Q_{m-1}$, the result being stated in terms of Gevrey classes $G^s$ with $1\leq sI documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
