Abstract. We consider the circle methods of summability theory (in discrete and continuous form). The basic Tauberian properties ($b$-equivalence, $O$-theorem) are treated in a short and lucid way. Thereby we employ logarithmic derivatives and M untz approximations.

AMS Subject Classification (1991): 40E10, 40G99, 40H05

Received February 15, 1999. (Registered under 2724/2009.)