Integral norm discretization and related problems

Abstract

The problem of replacing an integral norm with respect to a given probability measure by the corresponding integral norm with respect to a discrete measure is discussed in the paper. The above problem is studied for elements of finite dimensional spaces. Also, discretization of the uniform norm of functions from a given finite dimensional subspace of continuous functions is studied. We pay special attention to the case of the multivariate trigonometric polynomials with frequencies from a finite set with fixed cardinality. Both new results and a survey of known results are presented.

References in corpus (2)

• User-friendly tail bounds for sums of random matrices
• The Marcinkiewicz-type discretization theorems for the hyperbolic cross polynomials

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