Remark on the formula by Rakhmanov and Steklov's conjecture

2015/09/02 by S. A. Denisov, Denisov, S. A.
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA

paper · pdf · doi:10.48550/arxiv.1509.00819

arxiv created 2015/09/02 · arxiv updated 2015/09/03

Abstract

The conjecture by Steklov was solved negatively by Rakhmanov in 1979. His original proof was based on the formula for orthogonal polynomial obtained by adding point masses to the measure of orthogonality. In this note, we show how this polynomial can be obtained by applying the method developed recently for proving the sharp lower bounds for the problem by Steklov.

Related

• V.A. Steklov and the Problem of Sharp (Exact) Constants in Inequalities of Mathematical Physics
• The sharp estimates on the orthogonal polynomials from the Steklov class
• On Schur parameters in Steklov's problem
• On a problem by Steklov
• A proof of a conjecture about a symmetric system of orthogonal polynomials