Iterative reconstruction of multivariate band-limited functions from irregular sampling values
SIAM Journal on Mathematical Analysis
Efficient numerical methods in non-uniform sampling theory
Numerische Mathematik
Fast Local Reconstruction Methods for Nonuniform Sampling in Shift-Invariant Spaces
SIAM Journal on Matrix Analysis and Applications
Recent results on wavelet bases on the interval generated by GP refinable functions
Applied Numerical Mathematics - Applied scientific computing: Advances in grid generation, approximation and numerical modeling
Journal of Approximation Theory
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This paper concerns with iterative schemes for the perfect reconstruction from nonuniform sampling of functions belonging to multiresolution spaces on bounded manifolds. Since the iterations converge uniformly, we can produce the corresponding iterative integration schemes that allow to recover the integral of functions belonging to multiresolution spaces from nonuniform sampling. We present also an error analysis and, in particular, we estimate the L^2-error we produce in recovering smooth functions in H^s, but not necessarily in any multiresolution space. The error analysis extends to integrals. Our results hold regardless of the dimension of the domain and for a variety of multiresolution spaces constructed from certain refinable bases formed by the so-called GP-functions.