Research
Research
Embedded Files
My specific interests are in the areas of p-adic numbers, harmonic analysis, and problems in applied linear algebra, and engineering problems (scientific computing, signal processing, etc.).
My specific interests are in the areas of p-adic numbers, harmonic analysis, and problems in applied linear algebra, and engineering problems (scientific computing, signal processing, etc.).
Recently, I worked on Fourier analysis and equidistribution theory over the compact group of p-adic integers Zp. In collaboration with C. Petsche, we worked on some properties of real valued functions over Zp, and investigated various notions of finite variation. This work led to two recent papers
Recently, I worked on Fourier analysis and equidistribution theory over the compact group of p-adic integers Zp. In collaboration with C. Petsche, we worked on some properties of real valued functions over Zp, and investigated various notions of finite variation. This work led to two recent papers
Non-Archimedean Koksma inequalities, variation, and Fourier analysis (with Clayton Petsche). Uniform Distribution Theory, Vol.17, No. 22, 2022, 21- 50. (Journal, Open access).
A Leveque-type inequality on the ring of p-adic integers. International Journal of Number Theory, Vol. 18, No. 3, (2022), 655-671. (Journal). (An Arxiv version is available here).
A current project along a similar vein, with two other collaborators, involves studying the distribution of integer sequences modulo p^k for primes p, as well as in Zp with respect to some natural probability measures.
I am also working on a project tracing the evolution of the concept of Compactness in real analysis, using primary historical sources, which is nearing completion. This involved understanding the works of mathematicians of the nineteenth and early twentieth centuries, such as Dirichlet, Borel, Lebesgue, Frechet, and Hausdorff. Some of this research has been used to create a primary sources project to help undergraduate and beginning graduate students learn compactness, under the NSF funded TRIUMPHS project. See digitalcommons.ursinus.edu/triumphs_analysis/16.
I am also working on a project tracing the evolution of the concept of Compactness in real analysis, using primary historical sources, which is nearing completion. This involved understanding the works of mathematicians of the nineteenth and early twentieth centuries, such as Dirichlet, Borel, Lebesgue, Frechet, and Hausdorff. Some of this research has been used to create a primary sources project to help undergraduate and beginning graduate students learn compactness, under the NSF funded TRIUMPHS project. See digitalcommons.ursinus.edu/triumphs_analysis/16.
Google Sites
Report abuse