Barry Booton, Ph.D.
Senior Instructor
Charles E. Schmidt College of Science
Mathematics and Statistics
Boca Raton Campus | SE-43 286
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
- 鈥淎nother generalization of the Riemann-Stieltjes integral鈥, 16 pages.
- 鈥淩earrangements of general monotone functions and of their Fourier transforms鈥, 12 pages.
Peer-refereed articles in press
- 鈥淎lternate characterizations of bounded variation and of general monotonicity for functions鈥, Illinois Journal of Mathematics, to appear.
Peer-refereed articles in print
- 鈥淕eneral monotone functions and their Fourier coefficients鈥, Journal of Mathematical Analysis and Applications, Vol. 426, Issue 2, June 15, 2015, pp. 805-823.
- 鈥淕eneral monotone sequences and trigonometric series鈥, Mathematische Nachrichten, Vol. 287, Issues 5-6, April, 2014, pp. 518-529.
- 鈥淎symptotic behavior of Hardy operators鈥, with Yoram Sagher, Journal of Mathematical Inequalities, Vol. 5, Issue 3, Sept., 2011, pp. 383-400.
- 鈥淣orm inequalities for certain classes of functions and their Fourier transforms鈥, 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