On the convergence of orthorecursive expansions in nonorthogonal wavelets
Alexander Yurjevich Kudryavtsev · Mathematical Notes · 2012
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(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.