Existence of Multiwavelets in Rn

CABRELLI, CARLOS; GORDILLO, MARIA LUISA

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

AMER MATHEMATICAL SOC

Lugar: Providence; Año: 2001 vol. 130 p. 1413 - 1424

0002-9939

For a q-regular Multiresolution Analysis of multiplicity r with arbitrary dilation matrix A for a general lattice Γ in Rn, we give necessary and sufficient conditions in terms of the mask and the symbol of the vector scaling function in order that an associated wavelet basis exists. We also show that if 2r(m − 1) ≥ n where m is the absolute value of the determinant of A, then these conditions are always met, and therefore an associated wavelet basis of q-regular functions always exists. This extends known results to the case of multiwavelets in several variables with an arbitrary dilation matrix A for a lattice Γ.