Dr. Barry Booton
Education
- Ph.D. in Harmonic Analysis, University of Illinois at Chicago, 2005
Research Interests
- Harmonic Analysis
- Functions of one variable
Research Description
Much of my research has been in harmonic analysis. My focus has been on norm inequalities involving certain classes of functions (or sequences) and their Fourier transforms and coefficients (or corresponding trigonometric polynomials). The general monotone functions and sequences are particular classes of interest. More recently my work has been in functions of one variable; specifically, generalizing functions of bounded variation, and am in the process of developing some interesting applications for such functions.
Recent Publications
Peer-refereed articles under review
- “Another generalization of the Riemann-Stieltjes integral”, 16 pages.
- “Rearrangements of general monotone functions and of their Fourier transforms”, 12 pages.
Peer-refereed articles in press
- “Alternate characterizations of bounded variation and of general monotonicity for functions”, Illinois
Journal
of
Mathematics, to appear.
Peer-refereed articles in print
- “Rearrangements of general monotone functions and of their Fourier transforms”, Mathematical
Inequalities
and
Applications, Vol. 21, Issue 3, 2018, pp.871-883.
- “Alternate characterizations of bounded variation and of general monotonicity for functions”, Illinois
Journal
of
Mathematics, Vol. 60, Issue 2, 2016, pp. 551-561.
- “General monotone functions and their Fourier coefficients”, Journal
of
Mathematical
Analysis
and
Applications, Vol. 426, Issue 2, June 15, 2015, pp. 805-823.
- “General monotone sequences and trigonometric series”, Mathematische
Nachrichten, Vol. 287, Issues 5-6, April, 2014, pp. 518-529.
- “Asymptotic behavior of Hardy operators”, with Yoram Sagher, Journal
of
Mathematical
Inequalities, Vol. 5, Issue 3, Sept., 2011, pp. 383-400.
- “Norm inequalities for certain classes of functions and their Fourier transforms”, with Yoram Sagher, Journal
of
Mathematical
Analysis
and
Applications, Vol. 335, Issue 2, Nov. 15, 2007, pp. 1416-33
Scholarly Activities
Conferences and advanced courses attended
- Advanced Course in Constructive Approximation and Harmonic Analysis, CRM, Bellaterra (Barcelona), Spain, 2016
- Conference on Harmonic Analysis and Approximation Theory, CRM, Bellaterra (Barcelona), Spain, 2016
On top of a mountain overlooking Barcelona, Spain, 2016.
Dr. Booton enjoys riding his bicycle to Florida Atlantic University.
