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September 10, 2025Annales Polonici MathematiciOpen Access

Polynomials with exponents in compact convex sets and associated weighted extremal functions – The Bernstein–Walsh–Siciak theorem

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Authors

BMBenedikt Steinar MagnússonUniversity of Iceland RSRagnar SigurðssonUniversity of Iceland BSBergur SnorrasonUniversity of Iceland

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Implication

This research generalizes the bernstein-walsh-siciak theorem for polynomial approximation in compact convex sets, suggesting new methods for weighted error estimates.

Key Points

The study generalizes the bernstein-walsh-siciak theorem to include polynomials with exponents confined to compact convex sets.
New weighted uniform estimates are introduced, replacing traditional uniform estimates in polynomial approximation errors.
This framework broadens the understanding of polynomial rings by introducing a subring of polynomials with restricted exponents.
Implications of these findings suggest enhanced techniques for error assessment in mathematical approximations of functions.

Cite This Study

Magnússon et al. (2025) studied this question.

synapsesocial.com/papers/68c1bb6a54b1d3bfb60ed447 https://doi.org/10.4064/ap241204-30-7

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Implication

This research generalizes the bernstein-walsh-siciak theorem for polynomial approximation in compact convex sets, suggesting new methods for weighted error estimates.

Polynomials with exponents in compact convex sets and associated weighted extremal functions – The Bernstein–Walsh–Siciak theorem

Discussion

Member takes

Implication

Key Points

Cite This Study

Polynomials with exponents in compact convex sets and associated weighted extremal functions – The Bernstein–Walsh–Siciak theorem

Discussion

Member takes

Implication

Key Points

Cite This Study

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