One-sided Tauberian conditions for a general summability method
Let (u(n)) be a sequence of real numbers and L be an additive summability method with some property. We show that if slow decrease of (u(n)) or one-sided boundedness of the classical control modulo of the oscillatory behavior of (u(n)) is a Tauberian condition for a general summability method L, then one-sided boundedness by a sequence with certain conditions of the general control modulo of the oscillatory behavior of integer order m of (u(n)) is also a Tauberian condition for L. (C) 2011 Elsevier Ltd. All rights reserved.
tauberian conditions general summability method slow decrease general control modulo moderate oscillation one-sided bounded sequence