Abstract
UDC 517.5
Let
(
u
k
)
be a sequence of real or complex numbers. First, we consider a real sequence
(
u
k
)
and formulate one-sided Tauberian conditions, which are necessary and sufficient for the convergence of certain subsequences of
(
u
k
)
to follow from its deferred weighted summability. These conditions are satisfied if
(
u
k
)
is deferred slowly decreasing or if
(
u
k
)
obeys a Landau-type Tauberian condition. Second, we consider a complex sequence
(
u
k
)
and present a two-sided Tauberian condition which is necessary and sufficient in order that the convergence of certain subsequences of
(
u
k
)
follow from its deferred weighted summability. This condition is satisfied either if
(
u
k
)
is deferred slowly oscillating or if
(
u
k
)
obeys a Hardy-type Tauberian condition. Finally, we extend these results to sequences in ordered linear spaces over the real numbers.
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
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