On Existence of Matrix-Valued Wavelets
Wavelet analysis has been a powerful tool for exploring and solving many complicated problems in natural science and engineering computation. In this paper, we investigate the existence of matrix-valued wavelet associated with a matrix-valued multireslution analysis. By using operator polar decomposition, we provide a new proof for the existence of matrix-valued wavelets. We prove that, like in the scalar case, every matrix-valued multiresolution analysis guarantees the existence of an orthogonal matrix-valued wavelet.
Helen Zhang and David Jin
B. M. Yu, "On Existence of Matrix-Valued Wavelets", Advanced Materials Research, Vols. 282-283, pp. 153-156, 2011