Bilinear biorthogonal expansions and the Dunkl kernel on the real line

  1. Abreu, L.D. 2
  2. Ciaurri, T. 1
  3. Varona, J.L. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Universidade de Coimbra
    info

    Universidade de Coimbra

    Coímbra, Portugal

    ROR https://ror.org/04z8k9a98

Revista:
Expositiones Mathematicae

ISSN: 0723-0869

Any de publicació: 2012

Volum: 30

Número: 1

Pàgines: 32-48

Tipus: Article

DOI: 10.1016/J.EXMATH.2011.08.001 SCOPUS: 2-s2.0-84857441837 WoS: WOS:000302894300003 arXiv: 0909.0067 GOOGLE SCHOLAR lock_openAccés obert editor

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Ortogonalidad, Teoría de la Aproximación y sus aplicaciones en Ciencia y Tecnología

2009/00206/001

Resum

We study an extension of the classical Paley-Wiener space structure, which is based on bilinear expansions of integral kernels into biorthogonal sequences of functions. The structure includes both sampling expansions and Fourier-Neumann type series as special cases, and it also provides a bilinear expansion for the Dunkl kernel (in the rank 1 case) which is a Dunkl analogue of Gegenbauer's expansion of the plane wave and the corresponding sampling expansions. In fact, we show how to derive sampling and Fourier-Neumann type expansions from the results related to the bilinear expansion for the Dunkl kernel. © 2011 Elsevier Ltd. All rights reserved.