Inequalities for the Zeros of an Orthogonal Expansion of a Polynomial
Turán pointed out the importance of studying the location of the zeros of a polynomial in terms of the coefficients of an orthogonal expansion. He himself obtained numerous results for the Hermite expansion. Later Specht showed in a series of papers that analogous theorems hold for any expansion with respect to a system of polynomials orthogonal on the real line. His work stimulated various further studies. We give a survey on this topic with special emphasis on some results from an unpublished manuscript of Specht and new contributions by the author.
Key words and phrasesInequalities Zeros Bound of zeros Orthogonal Expansion Algebraic polynomials Orthogonal polynomials Norm estimates
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