Qingtang Jiang

Multivariate matrix refinable functions with arbitrary matrix dilation

Characterizations of the stability and orthonormality of a multivariate matrix refinable function D with arbitrary matrix dilation M are provided in terms of the eigenvalue and 1-eigenvector properties of the restricted transition operator. Under mild conditions, it is shown that the approximation order of D is equivalent to the order of the vanishing moment conditions of the matrix refinement mask {Pa}. The restricted transition operator associated with the matrix refinement mask {Pa } is represented by a finite matrix (Ami-j)i,j, with A -Idet(M)I-1 E, P-j Q3 P,E and P,-j Q3 P, being the Kronecker product of matrices P,-j and P,. The spectral properties of the transition operator are studied. The Sobolev regularity estimate of a matrix refinable function 4 is given in terms of the spectral radius of the restricted transition operator to an invariant subspace. This estimate is analyzed in an example.

Spectral Analysis of the Transition Operator and Its Applications to Smoothness Analysis of Wavelets

This paper investigates spectral properties of the transition operator associated to a multivariate vector refinement equation and their applications to the study of smoothness of the corresponding refinable vector of functions. Let

On the design of multifilter banks and orthonormal multiwavelet bases

\Phi=(\phi_1,\ldots,\phi_r)^T

Orthogonal multiwavelets with optimum time-frequency resolution

be an

Parameterizations of Masks for Tight Affine Frames with Two Symmetric/Antisymmetric Generators

r \times 1

On the regularity of matrix refinable functions

vector of compactly supported functions in

Parameterization of m‐channel orthogonal multifilter banks

L_2(\Rs)

Triangular √3-subdivision schemes: the regular case

satisfying

Surface subdivision schemes generated by refinable bivariate spline function vectors

\,\Phi = \sum_{\ga\in\Zs} a(\ga) \Phi({M\kern .1em \cdot}-\ga)

Convergence of cascade algorithms in Sobolev spaces and integrals of wavelets

, where M is an expansive integer matrix. The smoothness of