The bilinear Hilbert transform acting on Hermite and Laguerre functions

  • Authors:

  • Javier Duoandikoetxea

  • Affiliations:

  • Departamento de Matemáticas, Universidad del País Vasco-Euskal Herriko Unibertsitatea, Apartado 644, 48080 Bilbao, Spain

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2010

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Abstract

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.