Approximation of functions by n-separate wavelets in the spaces Lp (R), 1 ≤ p ≤ ∞

We consider the orthonormal bases of n-separate MRAs and wavelets constructed by the author earlier. The classical wavelet basis of the space L-2 (R) is formed by shifts and compressions of a single function psi. In contrast to the classical case, we consider a basis of L-2 (R) formed by shifts and compressions of n functions psi(s), s = 1,. . . , n. The constructed n-separate wavelets form an orthonormal basis of L-2(R). In this case, the series Sigma(n)(s=1) Sigma(j is an element of z) Sigma(k is an element of Z)(f, psi(s)(nj+s))psi(s)(nj+s) converges to the function f in the space L-2(R). We write additional constraints on the functions psi(s) and psi(s), s = 1, . . . , n, that provide the convergence of the series to the function f in the spaces L-p (R), 1 <= p <= 8, in the norm and almost everywhere.