In this paper, the notion of orthogonal vector-valued wavelet packets of space L2 (R^s, C^n) is introduced. A procedure for constructing the orthogonal vector-valued wavelet packets is presented. Their properties ar...In this paper, the notion of orthogonal vector-valued wavelet packets of space L2 (R^s, C^n) is introduced. A procedure for constructing the orthogonal vector-valued wavelet packets is presented. Their properties are characterized by virtue of time-frequency analysis method, matrix theory and finite group theory, and three orthogonality formulas are obtained. Finally, new orthonormal bases of space L2(R^s,C^n) are extracted from these wavelet packets.展开更多
In this work, the well-known problem put forward by S N Bernstein in 1930 is studied in a deep step. An operator is constructed by revising double interpolation nodes. It is proved that the operator converges to arbit...In this work, the well-known problem put forward by S N Bernstein in 1930 is studied in a deep step. An operator is constructed by revising double interpolation nodes. It is proved that the operator converges to arbitrary continuous functions uniformly and the convergence order is the best.展开更多
New higher dimensional distributions are introduced in the framework of Clifford analysis.They complete the picture already established in previous work, offering unity and structuralclarity. Amongst them are the buil...New higher dimensional distributions are introduced in the framework of Clifford analysis.They complete the picture already established in previous work, offering unity and structuralclarity. Amongst them are the building blocks of the principal value distribution, involvingspherical harmonics, considered by Horvath and Stein.展开更多
基金Foundation item: Supported by the Natural Science Foundation of China(10571113)
文摘In this paper, the notion of orthogonal vector-valued wavelet packets of space L2 (R^s, C^n) is introduced. A procedure for constructing the orthogonal vector-valued wavelet packets is presented. Their properties are characterized by virtue of time-frequency analysis method, matrix theory and finite group theory, and three orthogonality formulas are obtained. Finally, new orthonormal bases of space L2(R^s,C^n) are extracted from these wavelet packets.
基金Foundation item: Supported by the National Natural Science Foundation of China(10626045)
文摘In this work, the well-known problem put forward by S N Bernstein in 1930 is studied in a deep step. An operator is constructed by revising double interpolation nodes. It is proved that the operator converges to arbitrary continuous functions uniformly and the convergence order is the best.
文摘New higher dimensional distributions are introduced in the framework of Clifford analysis.They complete the picture already established in previous work, offering unity and structuralclarity. Amongst them are the building blocks of the principal value distribution, involvingspherical harmonics, considered by Horvath and Stein.