Remarks on orthogonal polynomials with respect to varying measures and related problems
We point out the relation between the orthogonal polynomials with respect to (w.r.t.) varying measures and the so-called orthogonal rationals on the unit circle in the complex plane. This observation enables us to combine different techniques in the study of these polynomials and rationals. As an ex...
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| Format: | Article |
| Language: | English |
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Wiley
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171293000298 |
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| _version_ | 1832560500572946432 |
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| author | Xin Li |
| author_facet | Xin Li |
| author_sort | Xin Li |
| collection | DOAJ |
| description | We point out the relation between the orthogonal polynomials with respect to
(w.r.t.) varying measures and the so-called orthogonal rationals on the unit circle in the complex
plane. This observation enables us to combine different techniques in the study of these
polynomials and rationals. As an example, we present a simple and short proof for a known result
on the weak-star convergence of orthogonal polynomials w.r.t, varying measures. Some related
problems are also considered. |
| format | Article |
| id | doaj-art-fea1051af98844c89f94190f5a8babca |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1993-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-fea1051af98844c89f94190f5a8babca2025-02-03T01:27:29ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251993-01-0116225525810.1155/S0161171293000298Remarks on orthogonal polynomials with respect to varying measures and related problemsXin Li0Department of Mathematics, University of Central Florida, Orlando 32816, FL, USAWe point out the relation between the orthogonal polynomials with respect to (w.r.t.) varying measures and the so-called orthogonal rationals on the unit circle in the complex plane. This observation enables us to combine different techniques in the study of these polynomials and rationals. As an example, we present a simple and short proof for a known result on the weak-star convergence of orthogonal polynomials w.r.t, varying measures. Some related problems are also considered.http://dx.doi.org/10.1155/S0161171293000298orthogonal polynomial and rationalweak-star convergence. |
| spellingShingle | Xin Li Remarks on orthogonal polynomials with respect to varying measures and related problems International Journal of Mathematics and Mathematical Sciences orthogonal polynomial and rational weak-star convergence. |
| title | Remarks on orthogonal polynomials with respect to varying measures and related problems |
| title_full | Remarks on orthogonal polynomials with respect to varying measures and related problems |
| title_fullStr | Remarks on orthogonal polynomials with respect to varying measures and related problems |
| title_full_unstemmed | Remarks on orthogonal polynomials with respect to varying measures and related problems |
| title_short | Remarks on orthogonal polynomials with respect to varying measures and related problems |
| title_sort | remarks on orthogonal polynomials with respect to varying measures and related problems |
| topic | orthogonal polynomial and rational weak-star convergence. |
| url | http://dx.doi.org/10.1155/S0161171293000298 |
| work_keys_str_mv | AT xinli remarksonorthogonalpolynomialswithrespecttovaryingmeasuresandrelatedproblems |