Al Boggess’ research is in the areas of analytic functions of a complex variable and Fourier analysis. An analytic function should be thought of as a generalization of a polynomial (with an infinite number of terms). Likewise, a Fourier series is an infinite sum of trigonometric terms. Analytic functions and Fourier series are the building blocks that can be used to approximate and construct more complicated mathematical functions. Although the origins of these subjects go back nearly two centuries and were largely motivated by mathematical curiosity, these subjects now play an essential role in scientific and engineering applications such as signal analysis and image reconstruction. In addition to many papers on the subjects of analytic functions and Fourier analysis, Al Boggess has co-authored an undergraduate/graduate text book on Fourier analysis and wavelets.
Education
Ph.D. Rice University 1979
Publications
Al Boggess, R. Dwilewicz and Z. Slodkowski. Hartogs-type extension for tube-like domains in C^2. Math. Annalen, (2014).
A. Boggess and A. Raich. "Heat kernels, smoothness estimates and exponential decay", with Albert Boggess. J. Fourier Analysis and Applications (2013).
A. Boggess and A. Raich. Fundamental Solutions to Box-b on Certain Quadrics. J. Geom. Analysis, 23(4):1729-1752, 2013 (2013).
A. Boggess, R. Dwilewicz and Z. Slodkowski. Hartogs Extension for Generalized Tubes in C^n. Journal of Mathematical Analysis and Applications (2013).
Albert Boggess, Roman Dwilewicz and Zbigniew Slodkowski. Hartogs Phenomenon on Unbounded Domains - Conjectures and Examples,. Centre de Recherches Mathématiques CRM Proceedings and Lecture Notes Volume 55, 2012 (2012).
Al Boggess. Survey of Recent Work on Estimates for the Solutions of Box-b and the Box-b Heat Equation. Invited Lecture at University of Arkansas Spring Lecture Series (Apr 2014).
A. Boggess. Unbounded Hartogs Domains. Invited Special Session Talk; AMS Sectional Meeting at Temple University (Oct 2013).
Albert Boggess. Extendability of Holomorphic Functions in Several Complex Variables. Colloquium at Missouri Institute of Technology (Apr 2012).
Albert Boggess (reporting on work joint with Andrew Raich). Fundamental Solutions for $\Box_b$ on Quadrics; January, 2012. Colloquium at the University of New England, Armidale, Australia (Jan 2012).
Service
Organization Committee - First Year Forward, member (2014 - Present)
Associate Editor for Complex Analysis and its Synergies, associate editor (2013 - Present)
Associate Editor for Complex Analysis and its Synergies, Associarte Editor (2013 - Present)
Natural Sciences Chairs/Directors Committee, member - as director of the School of Mathematical and Statistical Sciences (2012 - Present)
