On divergence of series of exponents representing functions regular in convex polygons
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.
English version (Springer): Ukrainian Mathematical Journal 46 (1994), no. 4, pp 471-474.
Citation Example: Mel'nik Yu. I. On divergence of series of exponents representing functions regular in convex polygons // Ukr. Mat. Zh. - 1994. - 46, № 4. - pp. 443–445.