summability sentence in Hindi
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- More generally, the operator should be in some p-trace class provided some summability on f holds; I guess f \ in O \ left ( \ exp (-c \ sqrt { n } ) \ right ) as you say should give you that with no pain, even for p = 1 ( so the operator is a 19 : 36, 16 January 2010 ( UTC)
- The greater generality of this result respect to the former one is due to the fact it proves the exact equivalence between ordinary convergence on one side and Abel summability ( condition 1 ) jointly with Tauberian condition ( condition 2 ) on the other . claims that this latter result must have appeared to Tauber much more complete and satisfying respect to the as it states a necessary and sufficient condition for the convergence of a series while the former one was simply a stepping stone to it : the only reason why Tauber's second theorem is not mentioned very often seems to be that it has no profound generalization as the first one has, though it has its rightful place in all detailed developments of summability of series.
- The greater generality of this result respect to the former one is due to the fact it proves the exact equivalence between ordinary convergence on one side and Abel summability ( condition 1 ) jointly with Tauberian condition ( condition 2 ) on the other . claims that this latter result must have appeared to Tauber much more complete and satisfying respect to the as it states a necessary and sufficient condition for the convergence of a series while the former one was simply a stepping stone to it : the only reason why Tauber's second theorem is not mentioned very often seems to be that it has no profound generalization as the first one has, though it has its rightful place in all detailed developments of summability of series.
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