Сибирский федеральный университет

Тип публикации: статья из журнала

Год издания: 2018

Идентификатор DOI: 10.1134/S1064562418010131

Аннотация: The Puiseux series generated by the power function z = w (1/rho), where rho > 0,rho not equal 1, is considered. A version of the Plya-Bernstein theorem for an entire function of order rho not equal 1 and normal type is proposed and applied to describe the domain of analytic continuation of this series. The domain of summability of a "regular" Puiseux series is found (this is a many-sheeted "Borel polygon"); in the case rho = 1, the "one-sheeted" result of Borel is substantially extended. These results make it possible to describe domains of analytic continuation of the Puiseux expansions of popular many-sheeted functions (such as inverses of rational functions).

Журнал: DOKLADY MATHEMATICS

Выпуск журнала: Vol. 97, Is. 1

Номера страниц: 42-46

ISSN журнала: 10645624

Место издания: NEW YORK

Издатель: MAIK NAUKA/INTERPERIODICA/SPRINGER

• Maergoiz L.S. (Siberian Fed Univ, Krasnoyarsk 660041, Russia)

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