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 $(x,xi )inR^n$, the eigenvalues of the principal symbol $a(x,xi )$ of $A$ are eigenvalues of the operator $P(x,y,xi ,D_y)$.
A General Effective-Hamiltonian Method
MARTINEZ, ANDRE' GEORGES
2007
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 $(x,xi )inR^n$, the eigenvalues of the principal symbol $a(x,xi )$ of $A$ are eigenvalues of the operator $P(x,y,xi ,D_y)$.File in questo prodotto:
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