Extensions of modulation-dilation Bessel Systems in L2 (R+)

• Li, Ya-Nan ^[1] ; Li, Yun-Zhang ^[1]
  1. [1] Beijing University of Technology

     Beijing University of Technology

     China

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 75, Fasc. 2, 2024, págs. 361-377
• Idioma: inglés
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• Resumen

  • Due to not being a group under addition, admits no traditional wavelet or Gabor frames. This paper addresses a class of modulation-dilation frames (-frames) for . We obtain a -transform matrix-based expression of adding generators to generate -tight frames from a -Bessel sequences in ; and present criteria on with being a Parseval frame (an orthonormal basis) for an arbitrary Parseval frame sequence (an orthonormal sequence) in . Some examples are also presented.