Bridgewater State University
Mathematics Seminar
October 5, 2015, 3:30-4:30 PM

Speaker: Vignon Oussa
Title: A Survey of Frame Theory

Bases play a prominent role in Linear Algebra. A fixed basis can be regarded as a set of building blocks for a vector space, and as such any vector can be expanded in a unique way into a linear combination of the elements of the basis. This uniqueness property might seem attractive from a theoretical point of view. However, when it comes to applications, bases have serious limitations. For example, bases are not robust to erasures. On the other hand, frames are linear algebraic tools which resemble bases, but are much more flexible and therefore more useful. This talk will provide a basic introduction to frame theory. I will show how to construct various frames (tight frames, Parseval frames, group frames, frames which are maximally robust to erasures) in finite-dimensional vector spaces and I will present applications to signal transmission as well. This talk will be accessible to students. If time allows, I will also introduce frame theory in infinite-dimensional settings and present several open problems that may be suitable for undergraduate research.

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