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 $\varphi$. It is established that, under certain not too rigid constraints on the function $\varphi$, the expansion for any function $f\in L^2(\mathbb{R})$ converges to $f$ in $L^2(\mathbb{R})$. 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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