Sampling, Marcinkiewicz-Zygmund Inequalities, Approximation, and Quadrature Rules

09/17/2019

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by   Karlheinz Gröchenig, et al.

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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.