Christoffel functions,orthogonal polynomials,and Nevai's conjecture for Freud weights |
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| Authors: | A L Levin D S Lubinsky |
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| Institution: | 1. Department of Mathematics, The Open University of Israel, Ramat Aviv, P.O. Box 39328, 61392, Tel Aviv, Israel
2. Department of Mathematics, University of Witwatersrand, P.O. Wits 2050, Republic of South Africa
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| Abstract: | We obtain upper and lower bounds for Christoffel functions for Freud weights by relatively new methods, including a new way to estimate discretization of potentials. We then deduce bounds for orthogonal polynomials on thereby largely resolving a 1976 conjecture of P. Nevai. For example, let W:=e
–Q, whereQ: is even and continuous in, Q" is continuous in (0,  ) andQ
'>0 in (0, ), while, for someA, B,
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