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Stone's decomposition of the renewal measure via Banach-algebraic techniques

Author: M. S. Sgibnev
Journal: Proc. Amer. Math. Soc. 130 (2002), 2425-2430
MSC (2000): Primary 60K05
Published electronically: February 4, 2002
MathSciNet review: 1897469
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Abstract: A Banach-algebraic approach to Stone's decomposition of the renewal measure is discussed. Estimates of the rate of convergence in a key renewal theorem are given.

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Additional Information

M. S. Sgibnev
Affiliation: Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 90, 630090 Russia

Keywords: Stone's decomposition, renewal measure, asymptotic behavior, submultiplicative function, spread-out distribution, Banach algebra
Received by editor(s): August 25, 2000
Received by editor(s) in revised form: February 19, 2001
Published electronically: February 4, 2002
Additional Notes: This research was supported by Grant 99–01–00504 of the Russian Foundation of Basic Research.
Communicated by: Claudia M. Neuhauser
Article copyright: © Copyright 2002 American Mathematical Society