Resumen de Extensions of modulation-dilation Bessel Systems in L^2({\mathbb R}_+)

Ya-Nan Li, Yun-Zhang Li

• Due to \mathbb R_+=(0,\,\infty ) not being a group under addition, L^2(\mathbb R_+) admits no traditional wavelet or Gabor frames. This paper addresses a class of modulation-dilation frames (\mathcal MD-frames) for L^2(\mathbb R_+) . We obtain a \Theta -transform matrix-based expression of adding generators to generate \mathcal MD-tight frames from a \mathcal{M}\mathcal{D} -Bessel sequences in L^2({\mathbb R}_+) ; and present criteria on \Phi with \mathcal{M}\mathcal{D}(\Psi \cup \Phi ,\,a,\,b) being a Parseval frame (an orthonormal basis) for an arbitrary Parseval frame sequence (an orthonormal sequence) \mathcal{M}\mathcal{D}(\Psi ,\,a,\,b) in L^2(\mathbb R_+) . Some examples are also presented.