The Zeros of Orthogonal Polynomials and Markov–Bernstein Inequalities for Jacobi-Exponential Weights on (−1,1)
Let Ux=∏i=1rx−tipi, 0<p<∞, −1=tr<tr−1<⋯<t2<t1=1, r≥2, pi>−1/p, i=1,2,…,r, and W=e−Qx where Q:−1,1⟶0,∞. We give the estimates of the zeros of orthogonal polynomials for the Jacobi-Exponential weight WU on −1,1. In addition, Markov–Bernstein inequalities for the weight WU are also...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/7805730 |
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| _version_ | 1832547634828541952 |
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| author | Rong Liu |
| author_facet | Rong Liu |
| author_sort | Rong Liu |
| collection | DOAJ |
| description | Let Ux=∏i=1rx−tipi, 0<p<∞, −1=tr<tr−1<⋯<t2<t1=1, r≥2, pi>−1/p, i=1,2,…,r, and W=e−Qx where Q:−1,1⟶0,∞. We give the estimates of the zeros of orthogonal polynomials for the Jacobi-Exponential weight WU on −1,1. In addition, Markov–Bernstein inequalities for the weight WU are also obtained. |
| format | Article |
| id | doaj-art-5601c8c9698b4e6ba3b4284e48a9468e |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-5601c8c9698b4e6ba3b4284e48a9468e2025-02-03T06:43:59ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/78057307805730The Zeros of Orthogonal Polynomials and Markov–Bernstein Inequalities for Jacobi-Exponential Weights on (−1,1)Rong Liu0College of Computer and Information Sciences, Fujian Agriculture and Forestry University, Fuzhou, Fujian 350002, ChinaLet Ux=∏i=1rx−tipi, 0<p<∞, −1=tr<tr−1<⋯<t2<t1=1, r≥2, pi>−1/p, i=1,2,…,r, and W=e−Qx where Q:−1,1⟶0,∞. We give the estimates of the zeros of orthogonal polynomials for the Jacobi-Exponential weight WU on −1,1. In addition, Markov–Bernstein inequalities for the weight WU are also obtained.http://dx.doi.org/10.1155/2020/7805730 |
| spellingShingle | Rong Liu The Zeros of Orthogonal Polynomials and Markov–Bernstein Inequalities for Jacobi-Exponential Weights on (−1,1) Journal of Mathematics |
| title | The Zeros of Orthogonal Polynomials and Markov–Bernstein Inequalities for Jacobi-Exponential Weights on (−1,1) |
| title_full | The Zeros of Orthogonal Polynomials and Markov–Bernstein Inequalities for Jacobi-Exponential Weights on (−1,1) |
| title_fullStr | The Zeros of Orthogonal Polynomials and Markov–Bernstein Inequalities for Jacobi-Exponential Weights on (−1,1) |
| title_full_unstemmed | The Zeros of Orthogonal Polynomials and Markov–Bernstein Inequalities for Jacobi-Exponential Weights on (−1,1) |
| title_short | The Zeros of Orthogonal Polynomials and Markov–Bernstein Inequalities for Jacobi-Exponential Weights on (−1,1) |
| title_sort | zeros of orthogonal polynomials and markov bernstein inequalities for jacobi exponential weights on 1 1 |
| url | http://dx.doi.org/10.1155/2020/7805730 |
| work_keys_str_mv | AT rongliu thezerosoforthogonalpolynomialsandmarkovbernsteininequalitiesforjacobiexponentialweightson11 AT rongliu zerosoforthogonalpolynomialsandmarkovbernsteininequalitiesforjacobiexponentialweightson11 |