Abstract
Frequently, convergence of a function f: ℝ+ → X for t → ∞ implies convergence of an average of this function. Assertions of this type are called Abelian theorems. A theorem is called Tauberian if, conversely, convergence of the function is deduced from the convergence of an average.
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© 2001 Springer Basel AG
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Arendt, W., Batty, C.J.K., Hieber, M., Neubrander, F. (2001). Asymptotics of Laplace Transforms. In: Vector-valued Laplace Transforms and Cauchy Problems. Monographs in Mathematics, vol 96. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5075-9_4
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DOI: https://doi.org/10.1007/978-3-0348-5075-9_4
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-5077-3
Online ISBN: 978-3-0348-5075-9
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