no. 1
A tauberian theorem for Cesàro summability
Compositio Mathematica, Tome 35 (1977) no. 1, pp. 49-56. 
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     title = {A tauberian theorem for {Ces\`aro} summability},
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     volume = {35},
     number = {1},
     year = {1977},
     mrnumber = {450840},
     zbl = {0355.40010},
     language = {en},
     url = {http://archive.numdam.org/item/CM_1977__35_1_49_0/}
}
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Kuttner, B. A tauberian theorem for Cesàro summability. Compositio Mathematica, Tome 35 (1977) no. 1, pp. 49-56. http://archive.numdam.org/item/CM_1977__35_1_49_0/

[1] P.L. Butzer and H.G. Neuheuser: Auf Cesàro-Limitierungsverfahren eingeschränkte Tauberbedingungen. Monatsh. für Math. 69 (1965) 1-17. | MR | Zbl

[2] H.R. Pitt: A note on Tauberian conditions for Abel and Cesàro summability. Proc. American Math. Soc. 6 (1955) 616-619. | MR | Zbl

[3] G. Szegö: Orthogonal Polynomials. American Math. Soc. Colloquium publications, 23 (New York, 1939). | JFM

[4] E.J. Whittaker and G.N. Watson: Modem Analysis (fourth edition) Cambridge, 1927).