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Optimal learning of bandlimited functions from localized sampling. (English) Zbl 1180.65182

The core of this compactly written paper deals with the problem of learning a function in translation-invariant reproducing kernel Hilbert spaces. The main application is in the last section of the paper: an optimal algorithm for approximating bandlimited functions from localized sampling is established. In the univariate case upper and lower bound estimates for the approximation error are given.

MSC:

94A20 Sampling theory in information and communication theory
41A80 Remainders in approximation formulas
65T40 Numerical methods for trigonometric approximation and interpolation
42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
65D20 Computation of special functions and constants, construction of tables
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