Szegő transformations and Nth order associated polynomials on the unit circle
نویسندگان
چکیده
منابع مشابه
Szego transformations and Nth order associated polynomials on the unit circle
In this paperwe analyze the Stieltjes functions defined by the Szegő inverse transformation of a nontrivial probabilitymeasure supported on the unit circle such that the corresponding sequence of orthogonal polynomials is defined by either backward or forward shifts in their Verblunsky parameters. Such polynomials are called anti-associated (respectively associated) orthogonal polynomials. Thus...
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Stieltjes-type polynomials corresponding to measures supported on the unit circle T are introduced and their asymptotic properties away from T are studied for general classes of measures. As an application, we prove the convergence of an associated sequence of interpolating rational functions to the corresponding Carathéodory function. In turn, this is used to give an estimate of the rate of co...
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Stieltjes-type polynomials corresponding to measures supported on the unit circle T are introduced and their asymptotic properties away from T are studied for general classes of measures. As an application, we prove the convergence of an associated sequence of interpolating rational functions to the corresponding Carathéodory function. In turn, this is used to give an estimate of the rate of co...
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Using the well-known fact that the Fourier transform is unitary, we obtain a class of orthogonal polynomials on the unit circle from the Fourier transform of the Laguerre polynomials (with suitable weights attached). Some related extremal problems which arise naturally in this setting are investigated.
متن کاملSzegő and para-orthogonal polynomials on the real line: Zeros and canonical spectral transformations
We study polynomials which satisfy the same recurrence relation as the Szegő polynomials, however, with the restriction that the (reflection) coefficients in the recurrence are larger than one in modulus. Para-orthogonal polynomials that follow from these Szegő polynomials are also considered. With positive values for the reflection coefficients, zeros of the Szegő polynomials, para-orthogonal ...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2009
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2009.03.040