Local Bernstein theory, and lower bounds for Lebesgue constants
3 days ago
- #Lebesgue constants
- #Bernstein inequality
- #Lagrange interpolation
- Paper titled 'Local Bernstein theory, and lower bounds for Lebesgue constants' uploaded to arXiv.
- Motivated by Erdős' problem on Lagrange interpolation, the paper modifies classical Bernstein-type inequalities to obtain 'local' versions.
- Key results include localized versions of Bernstein's inequality for functions of exponential type and related estimates.
- Application to analysis of high-degree polynomials exhibiting 'local exponential type' behavior.
- Connection to Lagrange interpolation and Lebesgue constants, with sharp lower bounds established.
- Use of AI tools (AlphaEvolve, ChatGPT Pro) in the research process, including numerical confirmation and proof assistance.
- Final proofs involved traditional methods like contour integrals and the residue theorem.