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
DOI:
https://doi.org/10.1090/S0002-9939-2010-10633-0
Published electronically:
September 16, 2010
MathSciNet review:
2763747
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Abstract | References | Similar Articles | Additional Information
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.
- 1. David H. Bailey, Jonathan M. Borwein, Neil J. Calkin, Roland Girgensohn, D. Russell Luke, and Victor H. Moll, Experimental mathematics in action, A K Peters, Ltd., Wellesley, MA, 2007. MR 2320374
- 2. Neil Calkin, Julia Davis, Michelle Delcourt, Zebediah Engberg, Jobby Jacob, and Kevin James, Taking the convoluted out of Bernoulli convolutions: A discrete approach, submitted.
- 3. Børge Jessen and Aurel Wintner, Distribution functions and the Riemann zeta function, Trans. Amer. Math. Soc. 38 (1935), no. 1, 48–88. MR 1501802, https://doi.org/10.1090/S0002-9947-1935-1501802-5
- 4. Yuval Peres, Wilhelm Schlag, and Boris Solomyak, Sixty years of Bernoulli convolutions, Fractal geometry and stochastics, II (Greifswald/Koserow, 1998) Progr. Probab., vol. 46, Birkhäuser, Basel, 2000, pp. 39–65. MR 1785620
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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:
https://doi.org/10.1090/S0002-9939-2010-10633-0
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.
