Examples concerning Abel and Cesàro limits

Christopher J. Bishop; Eugene A. Feinberg; Junyu Zhang

doi:10.1016/j.jmaa.2014.06.017

Examples concerning Abel and Cesàro limits

Stony Brook University

Sun Yat-Sen University

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

This note describes examples of all possible equality and strict inequality relations between upper and lower Abel and Cesàro limits of sequences bounded above or below. It also provides applications to Markov Decision Processes.

Original language	English
Pages (from-to)	1654-1661
Number of pages	8
Journal	Journal of Mathematical Analysis and Applications
Volume	420
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2014.06.017
State	Published - Dec 15 2014

Keywords

Abel limit
Cesàro limit
Hardy-Littlewood theorem
Tauberian theorem

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10.1016/j.jmaa.2014.06.017

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title = "Examples concerning Abel and Ces{\`a}ro limits",

abstract = "This note describes examples of all possible equality and strict inequality relations between upper and lower Abel and Ces{\`a}ro limits of sequences bounded above or below. It also provides applications to Markov Decision Processes.",

keywords = "Abel limit, Ces{\`a}ro limit, Hardy-Littlewood theorem, Tauberian theorem",

author = "Bishop, \{Christopher J.\} and Feinberg, \{Eugene A.\} and Junyu Zhang",

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AU - Feinberg, Eugene A.

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AB - This note describes examples of all possible equality and strict inequality relations between upper and lower Abel and Cesàro limits of sequences bounded above or below. It also provides applications to Markov Decision Processes.

KW - Abel limit

KW - Cesàro limit

KW - Hardy-Littlewood theorem

KW - Tauberian theorem

UR - https://www.scopus.com/pages/publications/84905374678

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DO - 10.1016/j.jmaa.2014.06.017

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SP - 1654

EP - 1661

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Examples concerning Abel and Cesàro limits

Abstract

Keywords

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