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Tauberian conditions for a general limitable method
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Let (un)
be a sequence of real numbers, L
an additive
limitable method with some property, and and
different spaces of sequences related to each other.
We prove that if the classical control modulo of the oscillatory
behavior of (un) in is a Tauberian condition
for L, then the general control modulo of the oscillatory
behavior of integer order m of (un)
in or
is also a Tauberian condition for L.
Title: Tauberian conditions for a general limitable method
Description:
Let (un)
be a sequence of real numbers, L
an additive
limitable method with some property, and and
different spaces of sequences related to each other.
We prove that if the classical control modulo of the oscillatory
behavior of (un) in is a Tauberian condition
for L, then the general control modulo of the oscillatory
behavior of integer order m of (un)
in or
is also a Tauberian condition for L.
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