Orthogonal Multiwavelet Frames inL2Rd

Orthogonal Multiwavelet Frames in L 2 Rd

We characterize the orthogonal frames and orthogonal multiwavelet frames in L2 R with matrix dilations of the form Df x √ |detA|f Ax , where A is an arbitrary expanding d × d matrix with integer coefficients. Firstly, through two arbitrarily multiwavelet frames, we give a simple construction of a pair of orthogonal multiwavelet frames. Then, by using the unitary extension principle, we present ...

Multiwavelet Frames from Refinable Function Vectors

Starting from any two compactly supported d-refinable function vectors in ( L2(R) )r with multiplicity r and dilation factor d, we show that it is always possible to construct 2rd wavelet functions with compact support such that they generate a pair of dual d-wavelet frames in L2(R) and they achieve the best possible orders of vanishing moments. When all the components of the two real-valued d-...

Orthogonal Frames of Translates

Two Bessel sequences are orthogonal if the composition of the synthesis operator of one sequence with the analysis operator of the other sequence is the 0 operator. We characterize when two Bessel sequences are orthogonal when the Bessel sequences have the form of translates of a finite number of functions in L(R). The characterizations are applied to Bessel sequences which have an affine struc...

On Almost Orthogonal Frames

Dual multiwavelet frames with symmetry from two-direction renable functions