Maria Charina

Regularity of anisotropic refinable functions

This paper presents a detailed regularity analysis of anisotropic wavelet frames and subdivision. In the univariate setting, the smoothness of wavelet frames and subdivision is well understood by means of the matrix approach. In the multivariate setting, this approach has been extended only to the special case of isotropic refinement with the dilation matrix all of whose eigenvalues are equal in the absolute value. The general anisotropic case has resisted to be fully understood: the matrix approach can determine whether a refinable function belongs to

Limits of level and parameter dependent subdivision schemes

C(mathbb{R}^s)

Multiple multivariate subdivision schemes: Matrix and operator approaches

or

System theory and orthogonal multi-wavelets

L_p(mathbb{R}^s)

Multigrid methods: Grid transfer operators and subdivision schemes

,

Anisotropic, interpolatory subdivision and multigrid

1 le p < infty

Anisotropic bivariate subdivision with applications to multigrid

, but its Holder regularity remained mysteriously unattainable. nIt this paper we show how to compute the Holder regularity in

System theory: learning orthogonal multi-wavelets

C(mathbb{R}^s)

Regularity of non-stationary subdivision: a matrix approach

or

Real algebraic geometry, moment problems and multivariate tight wavelet frames

L_p(mathbb{R}^s)