02-179 MARTINEZ Andre'
On a General Born--Oppenheimer Reduction Scheme (28K, LATeX 2e) Apr 10, 02
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Abstract. We perform a general reduction scheme that can be applied in particular to the spectral study of operators of the type $P=P(x,y,hD_x,D_y)$ as $h$ tends to zero. This scheme permits to reduce the study of $P$ to the one of a semiclassical matrix operator of the type $A=A(x,hD_x)$. Here, for any fixed $(x,\xi )\in\R^n$, the eigenvalues of the principal symbol $a(x,\xi )$ of $A$ are eigenvalues of the operator $P(x,y,\xi ,D_y)$.

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