Abstract. In 2003, F. Móricz proved that the jumps of a periodic function at its simple discontinuities can be determined by its conjugate Abel--Poisson mean. Later Q. L. Shi and X. L. Shi introduced the concentration factors method of Abel--Poisson type and established a criterion for functions that satisfied a condition of Dini type. For piecewise smooth functions the convergence rate of this method is usually faster then Móricz Process. In this paper we establish a new criterion for concentration factors without the condition of Dini type.
AMS Subject Classification
(1991): 42A50, 42A16
Keyword(s):
jump,
Abel--Poisson concentration factors,
convergence rate
Received July 12, 2008, and in revised form August 30, 2010. (Registered under 74/2010.)
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