Abstract
Wavelet analysis provides suitable bases for the class of L 2 functions. The function to be represented is approximated at different resolutions. The desirable properties of a basis are orthogonality, compact supportedness and symmetricity. In the scalar case, the only wavelet with these properties is Haar wavelet. Theory of multiwavelets assumes significance since it offers symmetric, compactly supported, orthogonal bases for L 2(R). The properties of a multiwavelet are determined by the corresponding Multiscaling Function. A multiscaling function is characterized by its symbol function which is a matrix polynomial in complex exponential. The inverse representation theorem of matrix polynomials provides a method to construct a matrix polynomial from its Jordan pair. Our objective is to find the properties that characterize a Jordan pair of a symbol function of a multiscaling function with desirable properties.
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Mubeen, M., Narayanan, V. (2014). Inverse Representation Theorem for Matrix Polynomials and Multiscaling Functions. In: Bandt, C., Barnsley, M., Devaney, R., Falconer, K., Kannan, V., Kumar P.B., V. (eds) Fractals, Wavelets, and their Applications. Springer Proceedings in Mathematics & Statistics, vol 92. Springer, Cham. https://doi.org/10.1007/978-3-319-08105-2_20
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