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August 20, 2025Proceedings of the American Mathematical Society

Average Nikolskii factors for random spherical polynomials

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Authors

YLYun LingJGJiaxin GengJLJiansong Li

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Overview

Analysis reveals the order of the average Nikolskii factor for spherical polynomials suggests intricate mathematical behavior in random functions.

Key Points

  • The average nikolskii factor shows constant order for spherical polynomials with specific coefficients, offering insights into their behavior.
  • In cases with bounded parameters, the average nikolskii factor order is of N^0, contrasting starkly with the worst case of N^(1/p-1/q).
  • A mathematical analysis evaluates spherical polynomials using orthonormal bases, illustrating properties of degree at most n.
  • Findings support further exploration of compact homogeneous spaces in relation to the nikolskii factors of these polynomials.

Cite This Study

Ling et al. (2025) studied this question.

synapsesocial.com/papers/68af4cd8ad7bf08b1ead63d8https://doi.org/10.1090/proc/17347
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