Certain classes of power series that cannot be analytically continued across their circle of convergence. (English. Russian original) Zbl 0907.30004

Pavlov, A. I.

Izv. Math. 61, No. 4, 795-812 (1997); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 61, No. 4, 119-136 (1997).

Since a pioneer theorem of Fabry in 1896, many papers have been devoted to give conditions under which an analytic function defined on \(| z | < 1\) by a power series cannot be analytically continued into the region \(| z| >1\), across any arc of the circle \(| z| =1\). The present paper enlarges the known class of power series that cannot be analytically continued in the above sense. Complete proofs are given and the paper presents a general picture of the history of the subject.

Reviewer: M.A.Jiménez (Puebla)

MSC:

30B40

Analytic continuation of functions of one complex variable

Keywords:

analytic continuation; power series