On divergence of series of exponents representing functions regular in convex polygons - Mel'nik, Yu. I.; Мельник, Ю. И.; Мельник, Ю. И. (Institute of Mathematics, NAS of Ukraine, 1994)
We prove that, on a convex polygon, there exist functions from the Smirnov class E whose series of exponents diverge in the metric of the space E. Similar facts are established for the convergence almost everywhere on the boundary of a polygon, for the uniform convergence on a closed polygon, and for the pointwise convergence at noncorner points of the boundary.