Local Convergence of Fourier Series with Respect to Periodized Wavelets Original Research Article

Fourier series with respect to wavelet orthonormal bases inL2([0, 1]m) for a wide class of multiresolution analyses are studied. Convergence at Lebesgue and strong Lebesgue points is investigated and sufficient conditions for a.e. convergence are found. In addition, similar conditions for a.e. convergence of wavelet expansions of non-periodic functions are obtained. The latter essentially improve known results.