La traza de Dixmier y el residuo de Wodzicki para operadores pseudodifferenciales globales sobre variedades compactas.

  • Duván Cardona Ghent University, Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent, Belgium.
  • César del Corral Universidad de los Andes, Department of Mathematics, Bogotá, Colombia.

Resumen

En esta nota se anuncian los resultados de nuestra investigación sobre la traza de Dixmier y el residuo de Wodzicki para operadores pseudodiferenciales sobre variedades compactas. Se calcula la traza de Dixmier y el residuo no conmutativo (residuo de Wodzicki) de operadores pseudodiferenciales invariantes sobre variedades compactas con o sin borde. Para cada variedad cerrada (suave, compacta y sin borde), se emplea la noción de símbolo global que viene dada por el análisis de Fourier asociado a cada operador elíptico y positivo (desarrollado por M. Ruzhansky and V. Turunen para para grupos de Lie y por M. Ruzhansky, N. Tokmagambetov y J. Delgado para variedades cerradas). En particular, para cada grupo de Lie compacto, se usa su teoría de representación. Respecto al análisis de operadores sobre variedades con borde, se usa el análisis no armónico asociado a problemas con valores de frontera (introducido por M. Ruzhansky, N. Tokmagambetov, y J. Delgado).

Palabras clave: Traza de Dixmier, residuo no conmutativo, operador global, teoría de representaciones

Citas

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Publicado
2020-02-14

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