Nearly one third of OBRECHKOFF”S works are in one of the most actively elaborated region of investigations in the classical analysis in the 20-th century namely the theory of divergent series.
OBRECHKOFF was skillful at the summation of such series and he was reputed as one of the greatest experts in this field. Being familiar to perfection with the classical methods of RIEMANN, CESARO, RIESZ, EULER-KNOPP, BOREL, MITTAG-LEFFLER and HAUSDORFF, he got deep results for the summation of the TAYLOR, DIRICHLET, FOURIER and LAPLACE series. He introduced also the absolute summation by the typical means of RIESZ and proved a number of precise TAUBERIAN theorems.
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