Title of article :
Strong Asymptotic Behavior and Weak Convergence of Polynomials Orthogonal on an Arc of the Unit Circle Original Research Article
Author/Authors :
M.Bello Hern?ndez، نويسنده , , E.Mi?a D??az، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2001
Pages :
23
From page :
233
To page :
255
Abstract :
Let σ be a finite positive Borel measure supported on an arc γ of the unit circle, such that σ′>0 a.e. on γ. We obtain a theorem about the weak convergence of the corresponding sequence of orthonormal polynomials. Moreover, we prove an analogue of the Szegő–Geronimus theorem on strong asymptotics of the orthogonal polynomials on the complement of γ, which completes to its full extent a result of N. I. Akhiezer. The key tool in the proofs is the use of orthogonality with respect to varying measures.
Journal title :
Journal of Approximation Theory
Serial Year :
2001
Journal title :
Journal of Approximation Theory
Record number :
851937
Link To Document :
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