Geodesic
Integral norm discretization and related problems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 74 (2019) no. 4, pp. 579-630

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The problem is discussed of replacing an integral norm with respect to a given probability measure by the corresponding integral norm with respect to a discrete measure. This problem is investigated for elements of finite-dimensional spaces. Also, discretization of the uniform norm of functions in a given finite-dimensional subspace of continuous functions is studied. Special attention is given to the case of multivariate trigonometric polynomials with frequencies (harmonics) in a finite set with fixed cardinality. Both new results and a survey of known results are presented. Bibliography: 47 titles.
Keywords: trigonometric polynomials, discretization, Marcinkiewicz-type theorems. 
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     author = {F. Dai and A. Prymak and V. N. Temlyakov and S. Yu. Tikhonov},
     title = {Integral norm discretization and related problems},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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     number = {4},
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     url = {http://geodesic.mathdoc.fr/item/RM_2019_74_4_a0/}
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F. Dai; A. Prymak; V. N. Temlyakov; S. Yu. Tikhonov. Integral norm discretization and related problems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 74 (2019) no. 4, pp. 579-630. http://geodesic.mathdoc.fr/item/RM_2019_74_4_a0/