The bilinear Hilbert transform acting on Hermite and Laguerre functions

• Autores: Francisco Javier Duoandikoetxea Zuazo
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 162, Nº 1, 2010, págs. 131-140
• Idioma: inglés
• DOI: 10.1016/j.jat.2009.03.009
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• Resumen

  • We obtain several formulas for the action of the bilinear Hilbert transform on pairs of Hermite and Laguerre functions. The results can be given as linear combinations of products of Hermite or Laguerre functions. We show also that for the generalized bilinear Hilbert transforms the results cannot be expressed in such a simple way.