JournalsrlmVol. 18, No. 3pp. 269–277

A general effective Hamiltonian method

  • André Martinez

    Università di Bologna, Italy
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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,hDx,Dy)P=P(x,y,hD_x,D_y) as hh tends to zero. This scheme permits to reduce the study of PP to the one of a semiclassical matrix operator of the type A=A(x,hDx)A=A(x,hD_x). Here, for any fixed (x,ξ)Rn(x,\xi )\in\R^n, the eigenvalues of the principal symbol a(x,ξ)a(x,\xi ) of AA are eigenvalues of the operator P(x,y,ξ,Dy)P(x,y,\xi ,D_y).

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André Martinez, A general effective Hamiltonian method. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 18 (2007), no. 3, pp. 269–277

DOI 10.4171/RLM/494