Geodesic
Tauberian Theorems for Cosine Operator Functions
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 474-480 
B. Jefferies; S. I. Piskarev. Tauberian Theorems for Cosine Operator Functions. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 474-480. http://geodesic.mathdoc.fr/item/TM_2002_236_a46/
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     title = {Tauberian {Theorems} for {Cosine} {Operator} {Functions}},
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     url = {http://geodesic.mathdoc.fr/item/TM_2002_236_a46/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The paper is devoted to the investigation of Cesaro-type averaging convergence for cosine operator functions acting on a Banach space $X$. It is shown that the behavior of Cesaro-type averaging for polynomially bounded cosine operator functions is completely defined by the behavior of the resolvent in a neighborhood of zero.

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