Elliptic polynomials orthogonal on the unit circle with respect to a singular continuous measure
نویسنده
چکیده
We introduce two explicit examples of polynomials orthogonal on the unit circle. Moments and the reflection coefficients are expressed in terms of Jacobi elliptic functions. We find explicit expression for these polynomials in terms of a new type of elliptic hypergeometric function. We show that obtained polynomials are orthogonal on the unit circle with respect to a positive measure which is singular continuous, i.e. it consists from infinite number points of increase which are dense on the unit circle. We construct also corresponding explicit systems of polynomials orthogonal on the interval of the real axis with respect to a singular continuous measure. They can be considered as an elliptic generalization of the Askey-Wilson polynomials of a special type.
منابع مشابه
Elliptic polynomials orthogonal on the unit circle with a dense point spectrum
We introduce two explicit examples of polynomials orthogonal on the unit circle. Moments and the reflection coefficients are expressed in terms of Jacobi elliptic functions. We find explicit expression for these polynomials in terms of a new type of elliptic hypergeometric function. We show that obtained polynomials are orthogonal on the unit circle with respect to a dense point meausure, i.e. ...
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