A non-power series approach to Wiman-Valiron type theorems (Q2790828)

Wiman-Valiron theory describes the behavior of entire functions near points of maximum modulus, using the Taylor series expansion. An alternative way to obtain such results is given by Macintyre's method of flat regions. \textit{W. Bergweiler, Ph. J. Rippon} and \textit{G. M. Stallard} [Proc. Lond. Math. Soc. (3) 97, No. 2, 368--400 (2008; Zbl 1174.37011)] further developed this method to cover not only entire functions, but also functions with a ``direct tract''.NEWLINENEWLINEIn the present paper the authors use these ideas to prove corresponding results for subharmonic functions \(u\) which are harmonic in certain disks around points \(z\) where \(u(z)\) is large.