Irregular wavelet frames and Gabor frames

CHRISTENSEN, O.; FAVIER, S.; ZÓ, F.

APPROXIMATION THEORY AND ITS APPLICATIONS

Springer Netherland

Lugar: Dordrecht; Año: 2001 vol. 17 p. 90 - 101

1000-9221

Given g 2 L2(IRn); we consider irregular wavelet systems of the form f¸ n 2 j g(¸jx ¡ kb)gj2ZZ;k2ZZn, where ¸j > 0 and b > 0. Su±cient conditions for the wavelet system to constitute a frame for L2(IRn) are given. For a class of functions g 2 L2(IRn) we prove that certain growth conditions on f¸jg will lead to frames, and that some other types of sequences exclude the frame property. We also give a su±cient condition for a Gabor system fe2¼ib(j;x)g(x ¡ ¸kgj2ZZn; k2ZZ to be a frame.g 2 L2(IRn); we consider irregular wavelet systems of the form f¸ n 2 j g(¸jx ¡ kb)gj2ZZ;k2ZZn, where ¸j > 0 and b > 0. Su±cient conditions for the wavelet system to constitute a frame for L2(IRn) are given. For a class of functions g 2 L2(IRn) we prove that certain growth conditions on f¸jg will lead to frames, and that some other types of sequences exclude the frame property. We also give a su±cient condition for a Gabor system fe2¼ib(j;x)g(x ¡ ¸kgj2ZZn; k2ZZ to be a frame.