Sampling, Marcinkiewicz-Zygmund Inequalities, Approximation, and Quadrature Rules
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Given a sequence of Marcinkiewicz-Zygmund inequalities in L^2, we derive approximation theorems and quadrature rules. The derivation is completely elementary and requires only the definition of Marcinkiewicz-Zygmund inequality, Sobolev spaces, and the solution of least square problems.
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