On asymptotic behavior of Heine-Stieltjes 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...
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| Format: | info:eu-repo/semantics/article |
| Language: | English |
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2012
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| Online Access: | http://hdl.handle.net/10835/1627 |
| _version_ | 1789406449567268864 |
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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:10835-1627 |
| institution | Universidad de Cuenca |
| language | English |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oai:repositorio.ual.es:10835-16272023-04-12T19:37:27Z On asymptotic behavior of Heine-Stieltjes and Van Vleck polynomials Martínez-Finkelshtein, Andrei Rakhmanov, Evgenii A. Comportamiento asintótico Heine-Stieltjes Polinomios Van Vleck Asymptotic behavior 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 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. 2012-08-01T07:36:06Z 2012-08-01T07:36:06Z 2010 info:eu-repo/semantics/article http://hdl.handle.net/10835/1627 en info:eu-repo/semantics/openAccess Contemporary Mathematics 507 (2010) |
| spellingShingle | Comportamiento asintótico Heine-Stieltjes Polinomios Van Vleck Asymptotic behavior Van Vleck polynomials Martínez-Finkelshtein, Andrei Rakhmanov, Evgenii A. On asymptotic behavior of Heine-Stieltjes and Van Vleck polynomials |
| title | On asymptotic behavior of Heine-Stieltjes and Van Vleck polynomials |
| title_full | On asymptotic behavior of Heine-Stieltjes and Van Vleck polynomials |
| title_fullStr | On asymptotic behavior of Heine-Stieltjes and Van Vleck polynomials |
| title_full_unstemmed | On asymptotic behavior of Heine-Stieltjes and Van Vleck polynomials |
| title_short | On asymptotic behavior of Heine-Stieltjes and Van Vleck polynomials |
| title_sort | on asymptotic behavior of heine-stieltjes and van vleck polynomials |
| topic | Comportamiento asintótico Heine-Stieltjes Polinomios Van Vleck Asymptotic behavior Van Vleck polynomials |
| url | http://hdl.handle.net/10835/1627 |
| work_keys_str_mv | AT martinezfinkelshteinandrei onasymptoticbehaviorofheinestieltjesandvanvleckpolynomials AT rakhmanovevgeniia onasymptoticbehaviorofheinestieltjesandvanvleckpolynomials |