A theorem which asserts that if a sequence or function behaves regularly, then some average of it behaves regularly. For example,
for any .
The converse is false, but can be made into a correct Tauberian
is subjected to an appropriate additional condition (Hardy 1999, p. 46).
See alsoTauberian Theorem
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ReferencesHardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York:
Chelsea, p. 46, 1999.
Referenced on Wolfram|AlphaAbelian Theorem
Cite this as:
Weisstein, Eric W. "Abelian Theorem."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AbelianTheorem.html