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Матем. сб., 1982, том 118(160), номер 1(5), страницы 104–117 (Mi msb2240)  

Эта публикация цитируется в 101 научных статьях (всего в 101 статьях)

Об асимптотике отношения ортогональных многочленов. II

Е. А. Рахманов


Аннотация: В работе доказано, что если положительная мера $\mu$, заданная на окружности $\Gamma=ż:|z|=1\}$, удовлетворяет условию $\mu'=\dfrac{d\mu}{d\theta}>0$ почти всюду на $\Gamma$, то для параметров $a_n=-\overline{\Phi_{n+1}(0)}$ соответствующих $\mu$ ортогональных многочленов $\Phi_n(z)=z^n+\cdots$ справедливо соотношение$\lim\limits_{n\to\infty}a_n=0$.
Библиография: 5 названий.

Полный текст: PDF файл (640 kB)
Список литературы: PDF файл   HTML файл

Англоязычная версия:
Mathematics of the USSR-Sbornik, 1983, 46:1, 105–117

Реферативные базы данных:

УДК: 517.5
MSC: 33A65, 42C05
Поступила в редакцию: 06.01.1982

Образец цитирования: Е. А. Рахманов, “Об асимптотике отношения ортогональных многочленов. II”, Матем. сб., 118(160):1(5) (1982), 104–117; E. A. Rakhmanov, “On the asymptotics of the ratio of orthogonal polynomials. II”, Math. USSR-Sb., 46:1 (1983), 105–117

Цитирование в формате AMSBIB
\RBibitem{Rak82}
\by Е.~А.~Рахманов
\paper Об асимптотике отношения ортогональных многочленов.~II
\jour Матем. сб.
\yr 1982
\vol 118(160)
\issue 1(5)
\pages 104--117
\mathnet{http://mi.mathnet.ru/msb2240}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=654647}
\zmath{https://zbmath.org/?q=an:0515.30030|0509.30028}
\transl
\by E.~A.~Rakhmanov
\paper On~the asymptotics of the ratio of orthogonal polynomials.~II
\jour Math. USSR-Sb.
\yr 1983
\vol 46
\issue 1
\pages 105--117
\crossref{https://doi.org/10.1070/SM1983v046n01ABEH002749}


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  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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