On asymptotic behavior of Heine-Stieljes and Van Vleck polynomials
We investigate the strong asymptotics of Heine-Stieltjes polynomials - polynomial solutions of a second order differential equations with complex polynomial coefficients. The solution is given in terms of critical measures (saddle points of the weighted logarithmic energy on the plane), that are tig...
| Main Authors: | , |
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| Format: | info:eu-repo/semantics/article |
| Language: | English |
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2017
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| Online Access: | http://hdl.handle.net/10835/4878 |
| _version_ | 1789406539806670848 |
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| author | Martínez-Finkelshtein, Andrei Rakhmanov, Evgenii A. |
| author_facet | Martínez-Finkelshtein, Andrei Rakhmanov, Evgenii A. |
| author_sort | Martínez-Finkelshtein, Andrei |
| collection | DSpace |
| description | We investigate the strong asymptotics of Heine-Stieltjes polynomials - polynomial solutions of a second order differential equations with complex polynomial coefficients. The solution is given in terms of critical measures (saddle points of the weighted logarithmic energy on the plane), that are tightly related to quadratic differentials with closed trajectories on the plane. The paper is a continuation of the research initiated in [arXiv:0902.0193]. However, the starting point here is the WKB method, which allows to obtain the strong asymptotics. |
| format | info:eu-repo/semantics/article |
| id | oai:repositorio.ual.es:10835-4878 |
| institution | Universidad de Cuenca |
| language | English |
| publishDate | 2017 |
| record_format | dspace |
| spelling | oai:repositorio.ual.es:10835-48782023-04-12T19:38:10Z On asymptotic behavior of Heine-Stieljes and Van Vleck polynomials Martínez-Finkelshtein, Andrei Rakhmanov, Evgenii A. We investigate the strong asymptotics of Heine-Stieltjes polynomials - polynomial solutions of a second order differential equations with complex polynomial coefficients. The solution is given in terms of critical measures (saddle points of the weighted logarithmic energy on the plane), that are tightly related to quadratic differentials with closed trajectories on the plane. The paper is a continuation of the research initiated in [arXiv:0902.0193]. However, the starting point here is the WKB method, which allows to obtain the strong asymptotics. 2017-06-21T10:03:03Z 2017-06-21T10:03:03Z 2010 info:eu-repo/semantics/article http://hdl.handle.net/10835/4878 en Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess First published in Contemporary Mathematics in 507, 209-232 (2010), published by the American Mathematical Society |
| spellingShingle | Martínez-Finkelshtein, Andrei Rakhmanov, Evgenii A. On asymptotic behavior of Heine-Stieljes and Van Vleck polynomials |
| title | On asymptotic behavior of Heine-Stieljes and Van Vleck polynomials |
| title_full | On asymptotic behavior of Heine-Stieljes and Van Vleck polynomials |
| title_fullStr | On asymptotic behavior of Heine-Stieljes and Van Vleck polynomials |
| title_full_unstemmed | On asymptotic behavior of Heine-Stieljes and Van Vleck polynomials |
| title_short | On asymptotic behavior of Heine-Stieljes and Van Vleck polynomials |
| title_sort | on asymptotic behavior of heine-stieljes and van vleck polynomials |
| url | http://hdl.handle.net/10835/4878 |
| work_keys_str_mv | AT martinezfinkelshteinandrei onasymptoticbehaviorofheinestieljesandvanvleckpolynomials AT rakhmanovevgeniia onasymptoticbehaviorofheinestieljesandvanvleckpolynomials |