On the Convergence of Orthorecursive Expansions in Nonorthogonal Wavelets

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 phi. It is established that, under certain not too rigid constraints on the function phi, the expansion for any function f is an element of L-2(R) converges to f in L-2(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. DOI: 10.1134/S0001434612110077