Perturbation of wavelet and Gabor frames

CARRIZO, I.; FAVIER, S.

Analysis in Theory and Applications

Springer Verlag

Lugar: Nanjing; Año: 2003 vol. 19 p. 238 - 254

1672-4070

In this work two aspects of theory of frames are presented. Given a suitable real sequence {lambda_j}{jin Z} we get necessary conditions on a function $phi in  L^2 (R)$ in order to the sequence $lambda_j^{1/2} phi (lambda_j x−kb)}j,kinZ$ be a frame in $L^2(R)$. Also we deal with frame stability when the dilation’s parameter or the mother of a wavelet frame is perturbed. For Gabor frames we obtain stability results on the generating function and on the translation’s parameter. In all cases we work without demanding compactness of the support, neither on the generating function, nor on his Fourier transform.