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Integral norm discretization and related problems

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arxiv 1807.01353 v3 pith:P3QHFFIN submitted 2018-07-03 math.NA cs.NA

F. Dai , A. Prymak , V. N. Temlyakov , S. Tikhonov This is my paper · ORCID
classification math.NAcs.NA
keywords normfiniteintegraldimensionaldiscretizationfunctionsgivenmeasure
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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.

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  1. Nonlinear approximation with adaptive dictionaries

    math.NA 2026-07 unverdicted novelty 5.0 of 10

    Sparse approximation of kernels with adaptive, kernel-dependent dictionaries controls sampling-recovery errors for families of integral-operator function classes.

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