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2010 GROWTH ORDERS OF CESÀRO AND ABEL MEANS OF FUNCTIONS IN BANACH SPACES
Jeng-Chung Chen, Ryotaro Sato, Sen-Yen Shaw
Taiwanese J. Math. 14(3B): 1201-1248 (2010). DOI: 10.11650/twjm/1500405913

Abstract

For continuous vector-valued functions, we discuss relations among exponential and polynomial growth orders of the $\gamma$-Cesàro mean ($\gamma \ge 0$) and of the Abel mean. In general, the Abel mean has growth order not larger than those of Cesàro means, and a higher-order Cesàro mean has a smaller growth order than a lower-order Cesàro mean. But, for a positive function in a Banach lattice, the Abel mean and all $\gamma$-Cesàro means with $\gamma \ge 1$ (but not with $0 \le \gamma \lt 1$) have the same polynomial growth order. The possibility of non-equal growth orders for these means is illustrated by some examples of $C_0$-semigroups and cosine operator functions.

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Jeng-Chung Chen. Ryotaro Sato. Sen-Yen Shaw. "GROWTH ORDERS OF CESÀRO AND ABEL MEANS OF FUNCTIONS IN BANACH SPACES." Taiwanese J. Math. 14 (3B) 1201 - 1248, 2010. https://doi.org/10.11650/twjm/1500405913

Information

Published: 2010
First available in Project Euclid: 18 July 2017

zbMATH: 1226.47011
MathSciNet: MR2674604
Digital Object Identifier: 10.11650/twjm/1500405913

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Rights: Copyright © 2010 The Mathematical Society of the Republic of China

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Vol.14 • No. 3B • 2010
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