On Uniform Boundedness and Uniform Asymptotics for Orthogonal Polynomials on the Unit Circle |
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Authors: | Boris Golinskii Leonid Golinskii |
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Affiliation: | Mathematical Division, Institute for Low Temperature Physics and Engineering, 47 Lenin Avenue, Kharkov, 310164, Ukraine |
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Abstract: | The known conditions due to G. Baxter, Ya. L. Geronimus, and B. L. Golinskii which guarantee the uniform boundedness and/or uniform asymptotic representation for orthonormal polynomials on the unit circle are under consideration. We show that these conditions are in general not necessary. We discuss the relation between the orthonormal polynomials on the unit circle, the best approximations, and absolutely convergent Fourier series. |
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