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In this paper, we introduce a class of vector-valued wavelet packets of space L2(Rs,Cv), which are generalizations of multivariate wavelet packets. A procedure for constructing a class of biorthogonal vector-valued higher-dimensional wavelet packets is presented and their biorthogonality properties are characterized by virtue of matrix theory, time-frequency analysis method, and operator theory. Three...
Wavelet analysis has been a powerful tool for exploring and solving many complicated problems in natural science and engineering computation. In this paper, the notion of orthogonal vector-valued wavelet packets with 3-scale in higher dimensions is introduced. A procedure for constructing them is presented. Their orthogonality property is characterized by virtue of finite group theory, time-frequency...
This paper establishes a clear procedure for finite-length beam problem and convection-diffusion equation solution via Haar wavelet technique. An operational matrix of integration based on the Haar wavelet is established,and the procedure for applying the matrix to solve the differential equations is formulated. The fundamental idea of Haar wavelet method is to convert the differential equations into...
In this paper, the notion of vector-valued multiresolution analysis and biorthogonal vector-valued wavelets is introduced. The existence of compactly supported biorthogonal vector-valued wavelets associated with a pair of biorthogonal compactly supported vector-valued scaling functions is investigated. An algorithm for constructing a class of biorthogonal compactly supported vector-valued wavelet...
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