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Tauberian Theorems for Integrals

Published online by Cambridge University Press:  20 November 2018

Ralph Henstock
Ralph Henstock*
Affiliation:
Queen's University, Belfast, N. Ireland
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When, for the generalized summation of series, we use A and B methods, giving A and B sums, respectively, we say that the A method is included in the B method, A ⊂ B, if the B sum exists and is equal to the A sum whenever the latter exists. A theorem proving such a result is called an Abelian theorem. For example, there is an Abelian theorem stating that if the A and B sums are the first Cesàro mean and the Abel mean, respectively, then A ⊂ B. If A ⊂ B and B ⊂ A, we say that A and B are equivalent, A = B. For example, the nth Hölder and nth. Cesàro means are equivalent.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 433 - 439
Copyright
Copyright © Canadian Mathematical Society 1963

References

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