the objective of this paper is to establish a complete characterization of multiwavelet packets associated with matrix dilation on general lattices $gamma$ in $mathbb r^d$ by virtue of time-frequency analysis, matrix theory and operator theory.

The objective of this paper is to establish a complete characterization of multiwavelet packets associated with matrix dilation on general lattices $Gamma$ in $mathbb R^d$ by virtue of time-frequency analysis, matrix theory and operator theory.

Let I be the 2 × 2 identity matrix, and M a 2 × 2 dilation matrix with M = 2I . First, we present the correlation of the scaling functions with dilation matrix M and 2I . Then by relating the properties of scaling functions with dilation matrix 2I to the properties of scaling functions with dilation matrix M , we give a parameterization of a class of bivariate nonseparable orthogonal symmetric ...

Glossary Dilation matrix A 2× 2 matrix M is called a dilation matrix if all the entries of M are integers and all the eigenvalues of M are greater than one in modulus. Isotropic dilation matrix A dilation matrix M is said to be isotropic if M is similar to a diagonal matrix and all its eigenvalues have the same modulus. Wavelet system A wavelet system is a collection of square integrable functi...

In this paper, we establish the asymptotic estimates for norms of matrix dilation operators on modulation spaces. As an application, study boundedness spaces Hausdorff operators. The definition are also revisited fitting our study.

We establish a finite-dimensional version of the Arveson-Stinespring dilation theorem for unital completely positive maps on operator systems. This result can be seen as general principle to deduce theorems from their classical infinite-dimensional counterparts. In addition providing unified proofs known theorems, we versions Agler's rational an annulus, Berger's operators numerical radius at m...