Construction of periodic wavelet frames with dilation matrix

An important tool for the construction of periodic wavelet frame with the help of extension principles was presented in the Fourier domain by Zhang and Saito [Appl. Comput. Harmon. Anal., 2008, 125： 68-186]. We extend their results to the dilation matrix cases in two aspects. We first show that the periodization of any wavelet frame constructed by the unitary extension principle formulated by Ron and Shen is still a periodic wavelet frame under weaker conditions than that given by Zhang and Saito, and then prove that the periodization of those generated by the mixed extension principle is also a periodic wavelet frame if the scaling functions have compact supports.     

HOMOGENIZATION,SYMMETRY, AND PERIODIZATION IN DIFFUSIVE RANDOM MEDIA

We present a systematic study of homogenization of diffusion in random media with emphasis on tile-based random microstructures.We give detailed examples of several such media starting from their physi...     

On Localization of Connective Covers

A result of Neisendorfer says that, for every connected p-complete finite complex Y with ₂Y torsion, the p-completion of P_{K(/p, 1)} (Ym) and Y are of the same homotopy type for any positive integer m. Here, P_{K(/p, 1)}(Ym) is the periodization functor of Bousfield and Ym) is the m-connective cover of the space Y. The proof of this result depends on Millers Theorem of Sullivans conjecture. The aim in this paper is to study the phenomenon without the use of Millers Theorem.AMS Subject Classification (2000): 55P60     

Gabor frames by sampling and periodization

By sampling the window of a Gabor frame for belonging to Feichtinger’s algebra, , one obtains a Gabor frame for . In this article we present a survey of results by R. Orr and A.J.E.M. Janssen and extend their ideas to cover interrelations among Gabor frames for the four spaces , , and . Some new results about general dual windows with respect to sampling and periodization are presented as well. This theory is used to show a new result of the Kaiblinger type to construct an approximation to the canonical dual window of a Gabor frame for .