Results 1 - 10 of 3578
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[en] In this paper we derive a formula for the rank of the self-commutator of hyponormal block Toeplitz operators TΦ with matrix-valued rational symbols Φ in L∞(Cnxn) via the classical Hermite-Fejer interpolation problem
[en] A generalization of the Mhaskar-Saff functional is obtained for a vector equilibrium problem with an external field. As an application, the supports of the equilibrium measures are found in a special vector equilibrium problem with Nikishin matrix.
[en] Bijective linear transformations of the matrix algebra over an arbitrary field that preserve simultaneous diagonalizability are characterized. This result is used for the characterization of bijective linear monotone transformations . Bibliography: 28 titles.
[en] Biorthogonal wavelets can be constructed from the biorthogonal scaling functions. In this note, we consider a inverse proposition in high dimension wavelet with arbitrary matrix dilation factor and prove that if the wavelets are biorthogonal, then the associated scaling functions should be biorthogonal.
[en] In this paper, we introduce matrix-valued multiresolution analysis and orthogonal matrix-valued wavelets with arbitrary integer dilation factor m. A necessary and sufficient condition on the existence of orthogonal matrix-valued wavelets is derived by virtue of paraunitary vector filter bank theory. An algorithm for constructing compactly supported m-scale orthogonal matrix-valued wavelets is presented. The notion of orthogonal matrix-valued wavelet packets is proposed. Their properties are investigated by means of time-frequency method, operator theory and matrix theory. In particular, it is shown how to construct various orthonormal bases of space L2(R, Crxr) from these wavelet packets, and the orthogonal decomposition relation is also given