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The density of the space of matrix-valued scaling functions. (Chinese. English summary) Zbl 1274.42088

Summary: Multiresolution analysis is very important for constructions of the wavelet basis. From the classic multiresolution analysis to the multiwavelets multiresolution analysis and the matrix-valued multiresolution analysis, the content of the MRA has been greatly development. In this paper, we discuss the density of the space of matrix-valued scaling functions based on the space of matrix-valued functions. Finally, we give two necessary and sufficient conditions and two sufficient conditions of the density.

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
65T60 Numerical methods for wavelets
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