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 classE whose series of exponents diverge in the metric of the spaceE. 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.