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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Discrete Bernoulli convolutions: An algorithmic approach toward bound improvement


Authors: Neil J. Calkin, Julia Davis, Michelle Delcourt, Zebediah Engberg, Jobby Jacob and Kevin James
Journal: Proc. Amer. Math. Soc. 139 (2011), 1579-1584
MSC (2010): Primary 05A16, 42A85; Secondary 26A46, 46G99, 28E99
Published electronically: September 16, 2010
MathSciNet review: 2763747
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Abstract: In this paper we consider a discrete version of the Bernoulli convolution problem traditionally studied via functional analysis. We develop an algorithm which bounds the Bernoulli sequences, and we give a significant improvement on the best known bound.


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Additional Information

Neil J. Calkin
Affiliation: Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634
Email: calkin@ces.clemson.edu

Julia Davis
Affiliation: Department of Mathematics, Grove City College, Grove City, Pennsylvania 16127
Address at time of publication: Dillsburg, Pennsylvania
Email: juliadavis87@gmail.com

Michelle Delcourt
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
Email: mdelcourt3@gatech.edu

Zebediah Engberg
Affiliation: Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755
Email: zeb@dartmouth.edu

Jobby Jacob
Affiliation: School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York 14623
Email: jxjsma@rit.edu

Kevin James
Affiliation: Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634
Email: kevja@clemson.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10633-0
PII: S 0002-9939(2010)10633-0
Keywords: Bernoulli convolution, Bernoulli sequence, growth rate of Bernoulli sequence
Received by editor(s): April 23, 2010
Received by editor(s) in revised form: May 23, 2010
Published electronically: September 16, 2010
Additional Notes: This research was supported by NSF grant DMS-0552799.
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.