Bernstein's theorem (polynomials)

inequality relating the maximum modulus of a complex polynomial function on the unit disk with the maximum modulus of its derivative on the unit disk
Intangible theorem Q25345912
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Bernstein's theorem (polynomials)

Summary

Bernstein's theorem (polynomials) is a theorem[1]. Bernstein's theorem (polynomials) draws 11 Wikipedia views per month (theorem category, ranking #275 of 1,306).[2]

Key Facts

  • Bernstein's theorem (polynomials) is credited with the discovery of Sergei Natanovich Bernstein[3].
  • Bernstein's theorem (polynomials)'s instance of is recorded as theorem[4].
  • Bernstein's theorem (polynomials)'s instance of is recorded as inequation[5].
  • Sergei Natanovich Bernstein is named after Bernstein's theorem (polynomials)[6].
  • Bernstein's theorem (polynomials)'s facet of is recorded as approximation theory[7].
  • Bernstein's theorem (polynomials)'s facet of is recorded as function of a complex variable[8].
  • Bernstein's theorem (polynomials)'s facet of is recorded as polynomial[9].
  • Bernstein's theorem (polynomials)'s different from is recorded as Bernstein's theorem[10].
  • Bernstein's theorem (polynomials)'s defining formula is recorded as \max_{|z| = 1} |P'(z)| \le n \max_{|z| = 1} |P(z)|[11].
  • Bernstein's theorem (polynomials)'s Google Knowledge Graph ID is recorded as /g/11bwc3wxk1[12].
  • Bernstein's theorem (polynomials)'s maintained by WikiProject is recorded as WikiProject Mathematics[13].
  • Bernstein's theorem (polynomials)'s Microsoft Academic ID is recorded as 2777905787[14].

Body

Works and Contributions

Bernstein's theorem (polynomials) is credited with the discovery of Sergei Natanovich Bernstein[3].

Why It Matters

Bernstein's theorem (polynomials) draws 11 Wikipedia views per month (theorem category, ranking #275 of 1,306).[2]

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [4] . wikidata.org.
  2. [5] . wikidata.org.
  3. [3] . wikidata.org.
  4. [6] . wikidata.org.
  5. [7] . wikidata.org.
  6. [8] . wikidata.org.
  7. [9] . wikidata.org.
  8. [10] . wikidata.org.
  9. [11] . wikidata.org.
  10. [12] . wikidata.org.
  11. [13] . wikidata.org.
  12. [14] . wikidata.org.

Class ancestry

  1. [1] . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] . Wikimedia Foundation. dumps.wikimedia.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). Bernstein's theorem (polynomials). Retrieved May 3, 2026, from https://4ort.xyz/entity/bernstein-s-theorem-polynomials-
MLA “Bernstein's theorem (polynomials).” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/bernstein-s-theorem-polynomials-.
BibTeX @misc{4ortxyz_bernstein-s-theorem-polynomials-_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Bernstein's theorem (polynomials)}}, year = {2026}, url = {https://4ort.xyz/entity/bernstein-s-theorem-polynomials-}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Bernstein's theorem (polynomials) — https://4ort.xyz/entity/bernstein-s-theorem-polynomials- (retrieved 2026-05-03)

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