Zhao, P., Zhao, C. (2016). The theory of matrix-valued multiresolution analysis frames. Bulletin of the Iranian Mathematical Society, 42(3), 507-519.

P. Zhao; C. Zhao. "The theory of matrix-valued multiresolution analysis frames". Bulletin of the Iranian Mathematical Society, 42, 3, 2016, 507-519.

Zhao, P., Zhao, C. (2016). 'The theory of matrix-valued multiresolution analysis frames', Bulletin of the Iranian Mathematical Society, 42(3), pp. 507-519.

Zhao, P., Zhao, C. The theory of matrix-valued multiresolution analysis frames. Bulletin of the Iranian Mathematical Society, 2016; 42(3): 507-519.

The theory of matrix-valued multiresolution analysis frames

Receive Date: 04 May 2016,
Accept Date: 04 May 2016

Abstract

A generalization of matrix-valued multiresolution analysis (MMRA) to matrix-valued frames, and the constructions of matrix-valued frames are considered and characterized. A matrix-valued frame multiresolution analysis is defined in this paper. We provide necessary and sufficient conditions for constructing matrix-valued frames and Riesz bases of translates, and give the calculation method of matrix-valued dual Riesz basis. These conclusions are useful in providing theoretical basis for constructing matrix-valued frames and Riesz basis.

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