On the cardinality of lower sets and universal discretization

Dai F.; Prymak A.; Shadrin A.Temlyakov V. N.Tikhonov S.

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On the cardinality of lower sets and universal discretization

机译：On the cardinality of lower sets and universal discretization

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A set Q in Z(+)(d) is a lower set if (k(1), ... , k(d)) is an element of Q implies (l(1), ...,l(d)) is an element of Q whenever 0 <= l(i) <= k(i) for all i. We derive new and refine known results regarding the cardinality of the lower sets of size n in Z(+)(d). Next we apply these results for universal discretization of the L-2-norm of elements from n-dimensional subspaces of trigonometric polynomials generated by lower sets. (c) 2022 Elsevier Inc. All rights reserved.

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《Journal of complexity》 |2023年第6期|101726.1-101726.16|共16页
作者
Dai F.; Prymak A.; Shadrin A.Temlyakov V. N.Tikhonov S.;
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作者单位

Univ Manitoba;

Univ Cambridge;

Univ South Carolina||Moscow Ctr Fundamental & Appl Math||Steklov Inst Math||Lomonosov Moscow State UnivCtr Recerca Matemat||ICREA||Univ Autonoma Barcelona;

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正文语种英语
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Lower sets; Downward closed sets; Integer partitions; Universal discretization; Multivariate trigonometric polynomials;

On the cardinality of lower sets and universal discretization

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