We consider a class of functions given by a class of generalized Fourier series which arise in the study of sampled-data control. These functions are continuous on the real line, but not differentiable at x=0. We prove that for all sufficiently small x > 0, these functions are larger than a constant times the square root of x.

Author Bio

Jonas Azzam is currently an undergraduate senior at the University ofNebraska-Lincoln. The summer after graduating high school, he attendedthe 2003 Nebraska REU in Appplied Mathematics, where much of the workon this paper was done.Since then he has continued research with Professor Richard Rebarber on a number of problems related toSampled-Data Control.

I am currently a third year graduate student at the University of Nebraska - Lincoln where I am working towards my doctorate degree.� My current interests in the mathematical field includes�difference equations and time scales.� When I worked on this project I had just completed my first year as a graduate student here at UNL, and I was a graduate student mentor for the project.�

Over the summer of 2003, Ian Grooms co-authored this paper at the REU site in Lincoln, Nebraska under the direction of Dr. Richard Rebarber. Since then Ian has aided in the research of Drs. Michael Lewis and Michael Trosset in optimization and multidimensional scaling at the College of William and Mary.� Ian will graduate from the College with a BS in Mathematics and plans to pursue graduate study in Applied Mathematics at the University of Colorado at Boulder starting in the fall of 2005.

Lincoln, NE, Gretchen Bartels was a graduate student�mentor in the summer�Nebraska Research Experience for Undergraduates�in Applied Mathematics.� Together with the other participants in the REU, under the direction of�Dr. Richard Rebarber, she aided in research for "A Nonstandard Fourier Inequality".� In May of 2004, Gretchen graduated with her Master's degree in Mathematics and is currently teaching mathematics�at the high school level�in Las Vegas, NV.� She hopes to someday return to graduate school and earn a Ph.D in mathematics education.

I am currently a PHD student in the Applied Math program at the University of Colorado.� The work he did on the paper was done at an REU Site during the summer of 2003 at University of Nebraska at Lincoln, where I was an undergraduate at the time.� It was a great experience with a lot of cooperation between the members of the group.� My future plans include getting my doctorate in Applied Mathematics and doing research in numerical analysis.