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Veronika Furst is an associate professor of mathematics at Fort Lewis College. She joined the college in 2007. Dr. Furst is a nominee of the U.S. Professors of the Year Award (2013), sponsored by the Council for Advancement and Support of Education and the Carnegie Foundation for the Advancement of Teaching. She has been selected twice as one of four mathematics scholars to teach in the competitive George Washington University Summer Program for Women in Mathematics. In addition to her own research, Dr. Furst advises Fort Lewis undergraduate research projects funded by the National Science Foundation and other organizations, independent study projects and senior theses on a variety of mathematics topics.
In 2014, Dr. Veronika Furst and Dr. Erich McAlister, both Associate Professors of Mathematics at FLC wrote Multiresolution Equivalence and Path-Connectedness for the Journal of Numerical Functional Analysis and Optimization, 35 (12), 1511-1531.
Abstract
An equivalence relation between multiresolution analyses was first introduced in 1996; an analogous definition for generalized multiresolution analyses was given in 2010. This article describes the relationship between the two notions and shows that both types of equivalence classes are path connected in an operator-theoretic sense. The GMRA paths are restricted to canonical GMRAs, and it is shown that whenever two MRAs in L 2(R) are equivalent, the GMRA path construction between their corresponding canonical GMRAs yields the natural analog of the MRA path. Examples are provided of GMRA paths that are distinct from MRA paths.
Dr. Furst Explains the Project
"The easiest way to think about a multi-resolution analysis is as the mathematics of zooming. If you think of an image, for example a picture of a tree, there is a lot of data contained in that image. If you want to text or email that picture to someone, how much data you have to send is important. The idea behind multi-resolution analysis is to think about that image first as a coarse approximation of the actual picture and then, at each level of added resolution, more and more details. For example, if all you need to know is that you’re looking at a picture of a tree, you don’t need too much data. If you need to know what kind of tree it is, then you’d want more data, corresponding to finer levels of resolution. Multi-resolution analysis is the mathematics behind breaking down an image in this way."