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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2004
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/math/0401415 |
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| _version_ | 1866917022847205376 |
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| author | Vertesi, P. Xu, Yuan |
| author_facet | Vertesi, P. Xu, Yuan |
| contents | For a family of weight functions that include the general Jacobi weight functions as special cases, exact condition for the convergence of the Fourier orthogonal series in the weighted $L^p$ space is given. The result is then used to establish a Marcinkiewicz-Zygmund type inequality and to study weighted mean convergence of various interpolating polynomials based on the zeros of the corresponding orthogonal polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0401415 |
| institution | arXiv |
| publishDate | 2004 |
| record_format | arxiv |
| spellingShingle | Mean convergence of orthogonal Fourier series and interpolating polynomials Vertesi, P. Xu, Yuan Numerical Analysis For a family of weight functions that include the general Jacobi weight functions as special cases, exact condition for the convergence of the Fourier orthogonal series in the weighted $L^p$ space is given. The result is then used to establish a Marcinkiewicz-Zygmund type inequality and to study weighted mean convergence of various interpolating polynomials based on the zeros of the corresponding orthogonal polynomials. |
| title | Mean convergence of orthogonal Fourier series and interpolating polynomials |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/math/0401415 |