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On the nuclear trace of Fourier integral operators

  • Cardona, Duván [1]
    1. [1] Ghent University

      Ghent University

      Arrondissement Gent, Bélgica

  • Localización: Integración: Temas de matemáticas, ISSN 0120-419X, Vol. 37, Nº. 2, 2019 (Ejemplar dedicado a: Revista Integración, temas de matemáticas), págs. 219-249
  • Idioma: inglés
  • DOI: 10.18273/revint.v37n2-2019002
  • Títulos paralelos:
    • Sobre la traza nuclear de operadores integrales de Fourier
  • Enlaces
  • Resumen
    • español

      En esta investigación se caracteriza la r-nuclearidad de operadoresintegrales de Fourier en espacios de Lebesgue. Las nociones de traza nuclear y operador nuclear sobre espacios de Banach son conceptos análogos a aquellas de traza espectral y de operador de clase traza en espacios de Hilbert. Operadores integrales de Fourier, por otro lado, surgen para expresar soluciones a problemas de Cauchy hiperbólicos o para estudiar la función espectral asociada a un operador geométrico sobre una variedad diferenciable. Los operadoresintegrales de Fourier se consideran actuando sobre Rn, el grupo discreto Zn, el toro de dimensión n y finalmente, espacios simétricos (variedades compactas homogéneas). Se presentan ejemplos explícitos de tales caracterizaciones sobre Zn, el grupo especial unitario SU(2), y el plano complejo proyectivo CP2. Los resultados principales de la presente investigación se aplican en la caracterización de operadores pseudo diferenciales nucleares definidos mediante el proceso de cuantificación de Wey l.

    • English

      In this paper we characterise the r-nuclearity of Fourier integraloperators on Lebesgue spaces. Fourier integral operators will be considered in Rn, the discrete group Zn, the n-dimensional torus and symmetric spaces (compact homogeneous manifolds). We also give formulae for the nuclear trace of these operators. Explicit examples will be given on Zn, the torus Tn, the special unitary group SU(2), and the projective complex plane CP2. Our main theorems will be applied to the characterization of r-nuclear pseudodifferential operators defined by the Weyl quantization procedure.

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