Affine, quasi-affine and co-affine frames on local fields of positive characteristic

摘要

The concept of quasi-affine frame in Euclidean spaces was introduced toobtain translation invariance of the discrete wavelet transform. We extend thisconcept to a local field $K$ of positive characteristic. We show that theaffine system generated by a finite number of functions is an affine frame ifand only the corresponding quasi-affine system is a quasi-affine frame. In sucha case the exact frame bounds are equal. This result is obtained by using theproperties of an operator associated with two such affine systems. Wecharacterize the translation invariance of such an operator. A related conceptis that of co-affine system. We show that there do not exist any co-affineframe in $L^2(K)$.