Orthogonal wavelets on direct products of cyclic groups |
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Authors: | Yu A Farkov |
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Institution: | (1) Russian State Geological Prospecting University, Russia |
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Abstract: | We describe a method for constructing compactly supported orthogonal wavelets on a locally compact Abelian group G which is the weak direct product of a countable set of cyclic groups of pth order. For all integers p, n ≥ 2, we establish necessary and sufficient conditions under which the solutions of the corresponding scaling equations with p n numerical coefficients generate multiresolution analyses in L 2(G). It is noted that the coefficients of these scaling equations can be calculated from the given values of p n parameters using the discrete Vilenkin-Chrestenson transform. Besides, we obtain conditions under which a compactly supported solution of the scaling equation in L 2(G) is stable and has a linearly independent system of “integer” shifts. We present several examples illustrating these results. |
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Keywords: | orthogonal wavelets multiresolution analysis scaling equation locally compact Abelian group cyclic group Walsh function Haar measure Borel set blocked set of a mask |
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