Lower Bounds for Lebesgue Constants and an Erdős-Turán Interpolation Problem
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Statement
Localizing Bernstein theory to prove lower bounds for the Lebesgue constants of Lagrange interpolation, with application to a problem of Erdős and Turán and to a conjectured bound from the interpolation literature.
Context
Erdős-Turán interpolation questions are classical approximation theory with nine decades of literature, known well beyond the immediate specialty.
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"After some experimentation using the tool AlphaEvolve, the author was led to conjecture a proof of (1.29) by separately lower bounding each of these two factors. The first of these conjectures was then proven by ChatGPT, and the author was able to prove the second, thus giving a complete proof." Figures generated by Gemini.
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