An accuracy improvement in Egorov's theorem.

Título inglés An accuracy improvement in Egorov's theorem.
Título español Una mejora en la precisión del teorema de Egorov.
Autor/es Silva, Jorge Drumond
Organización Dep. Math. Inst. Super. Tec., Lisboa, Portugal
Revista 0214-1493
Publicación 2007, 51 (1): 77-120, 19 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés We prove that the theorem of Egorov, on the canonical transformation of symbols of pseudodifferential operators conjugated by Fourier integral operators, can be sharpened. The main result is that the statement of Egorov's theorem remains true if, instead of just considering the principal symbols in Sm/Sm-1 for the pseudodifferential operators, one uses refined principal symbols in Sm/Sm-2, which for classical operators correspond simply to the principal plus the subprincipal symbol, and can generally be regarded as the first two terms of its Weyl symbol expansion: we call it the principal Weyl symbol of the pseudodifferential operator. Particular unitary Fourier integral operators, associated to the graph of the canonical transformation, have to be used in the conjugation for the higher accuracy to hold, leading to microlocal representations by oscillatory integrals with specific symbols that are given explicitly in terms of the generating function that locally describes the graph of the transformation. The motivation for the result is based on the optimal symplectic invariance properties of the Weyl correspondence in Rn and its symmetry for real symbols.
Clasificación UNESCO 120220
Palabras clave español Operadores pseudodiferenciales ; Símbolos ; Operadores integrales
Código MathReviews MR2307148
Icono pdf Acceso al artículo completo