On Localised Error Bounds for Orthogonalapproximation
نویسنده
چکیده
It is well known that a shift invariant space S(N) generated by a compactly supported function N whose integer translates are a Riesz basis of S(N) has a unique orthonormal basis generated by a fundamental function of exponential decay. This result is extended by showing how the localisation carries over to the error of the orthogonal approximation P f] from S(N), i.e. localised error bounds are proved of the type ! 2 L q (IR) and a radial function of exponential decay. Optimal choices for are characterised using the zeros of the generalised Euler-Frobenius polynomial.
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