A Two-Parameter Family of Orthogonal Polynomials with Respect to a Jacobi-Type Weight on the Unit Circle

Christer Glader

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A Two-Parameter Family of Orthogonal Polynomials with Respect to a Jacobi-Type Weight on the Unit Circle

机译：关于单位圆上的Jacobi型权重的两个多项式正交多项式族

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A two-parameter family of polynomials is introduced by a recursion formula. The polynomials are orthogonal on the unit circle with respect to the weight #omega#_(#alpha#, #beta#)(theta#) = |(1-z)~#alpha#(1+z)~#beta#|~2, #alpha#, #beta# > -1/2, z = e~(i#theta#). Explicit representation, norm estimates, shift identities, and explicit connection to Jacobi polynomials on the real interval [-1, 1] is presented.

机译：通过递归公式引入了两参数多项式族。多项式关于权重#omega #_（＃alpha＃，#beta＃）（theta＃）= |（1-z）〜＃alpha＃（1 + z）〜＃beta＃在单位圆上正交|〜2，＃alpha＃，＃beta＃> -1 / 2，z = e〜（i＃theta＃）。给出了在实区间[-1，1]上的显式表示，范数估计，移位恒等式以及与Jacobi多项式的显式连接。

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《Journal of Mathematical Analysis and Applications》 |1999年第2期|共17页
作者
Christer Glader;
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正文语种 eng
中图分类数学;
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1. A Two-Parameter Family of Orthogonal Polynomials with Respect to a Jacobi-Type Weight on the Unit Circle [J] . Christer Glader Journal of Mathematical Analysis and Applications . 1999,第2期

机译：关于单位圆上的Jacobi型权重的两个多项式正交多项式族
2. ORTHOGONAL POLYNOMIALS WITH RESPECT TO A FAMILY OF SOBOLEV INNER PRODUCTS ON THE UNIT CIRCLE [J] . Ranga A. Sri Proceedings of the American Mathematical Society . 2016,第3期

机译：关于单位圆上Sobolev内部产品族的正交多项式
3. The growth of polynomials orthogonal on the unit circle with respect to a weight w that satisfies w, w(-1) is an element of L-infinity(T) [J] . Denisov S. A. Sbornik. Mathematics . 2018,第7a8期

机译：相对于满足W，W（-1）的重量W对单位圆的多项式正交的生长是L-Infinity（T）的元素
4. Zero's Asymptotic Distribution of Polynomials Orthogonal with respect to Varying Weights [C] . M.X.He, P.Natalini, P.E.Ricci Guangzhou international symposium on advances in computational mathematics . 1999

机译：关于权重变化的正交多项式的零点的渐近分布
5. Orthogonal Polynomials on an Arc of the Unit Circle with Respect to a Generalized Jacobi Weight: A Riemann-Hilbert Method Approach. [D] . Naugle, Lynsey. 2017

机译：关于广义Jacobi权重的单位圆弧上的正交多项式：Riemann-Hilbert方法。
6. A Robust Handwritten Numeral Recognition Using Hybrid Orthogonal Polynomials and Moments [O] . Sadiq H. Abdulhussain, Basheera M. Mahmmod, Marwah Abdulrazzaq Naser, 2021

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7. A Two-Parameter Family of Orthogonal Polynomials with Respect to a Jacobi-Type Weight on the Unit Circle [O] . Glader Christer 1999

机译：关于单位圆上的Jacobi型权重的两个多项式正交多项式族
8. Resonance Zones in Two-Parameter Families of Circle Homeomorphisms [R] . Hall, G. R. 1983

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A Two-Parameter Family of Orthogonal Polynomials with Respect to a Jacobi-Type Weight on the Unit Circle

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