Sobre la traza nuclear de operadores integrales de Fourier

  • Duván Cardona Ghent University, Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent, Belgium.

Resumen

En esta investigación se caracteriza la r-nuclearidad de operadores
integrales 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 operadores
integrales 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.

Palabras clave: Operador integral de Fourier, operador nuclear, traza nuclear, traza espectral, variedad compacta homogénea

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Citas

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Publicado
2019-07-29