Fourier-like frames on locally compact abelian groups

• Ole Christensen ^[1] ; Say Song Goh ^[2]
  1. [1] Technical University of Denmark

     Technical University of Denmark

     Dinamarca

     
  2. [2] National University of Singapore

     National University of Singapore

     Singapur

     
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 192, Nº 1 (April 2015), 2015, págs. 82-101
• Idioma: inglés
• DOI: 10.1016/j.jat.2014.11.002
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• Resumen

  • We consider a class of functions, defined on a locally compact abelian group by letting a class of modulation operators act on a countable collection of functions. We derive sufficient conditions for such a class of functions to form a Bessel sequence or a frame and for two such systems to be dual frames. Explicit constructions are obtained via various generalizations of the classical B-splines to the setting of locally compact abelian groups.