Let f (z)=a 0 , 0 (z)+a 1 , 1 (z)+ } } } +a n , n (z) be a polynomial of degree n, given as an orthogonal expansion with real coefficients. We study the location of the zeros of f relative to an interval and in terms of some of the coefficients. Our main theorem generalizes or refines results due to
Markov′s Inequality and Zeros of Orthogonal Polynomials on Fractal Sets
✍ Scribed by A. Jonsson
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 378 KB
- Volume
- 78
- Category
- Article
- ISSN
- 0021-9045
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✦ Synopsis
Zeros of orthogonal polynomials defined with respect to general measures are studied. It is shown that a certain estimate for the minimal distance between zeros holds if and only if the support (F) of the measure satisfies a homogeneity condition and Markov's inequality holds on (F). C 1994 Academic Press, Inc.
📜 SIMILAR VOLUMES
## Abstract We prove that there is a universal measure on the unit circle such that any probability measure on the unit disk is the limit distribution of some subsequence of the corresponding orthogonal polynomials. This follows from an extension of a result of Alfaro and Vigil (which answered a qu