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.

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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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     author = {B. Jefferies and S. I. Piskarev},
     title = {Tauberian {Theorems} for {Cosine} {Operator} {Functions}},
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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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