On the convergence of orthorecursive expansions in nonorthogonal wavelets |
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Authors: | A Yu Kudryavtsev |
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Institution: | 1. Moscow State Institute of International Relations, Ministry of Foreign Affairs, Moscow, Russian Federation
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Abstract: | The present paper is concerned with orthorecursive expansions which are generalizations of orthogonal series to families of nonorthogonal wavelets, binary contractions and integer shifts of a given function φ. It is established that, under certain not too rigid constraints on the function φ, the expansion for any function f ∈ L 2(?) converges to f in L 2(?). Such an expansion method is stable with respect to errors in the calculation of the coefficients. The results admit a generalization to the n-dimensional case. |
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