Equal norm Parseval frames on vector bundles

An equal norm parseval frame is a generalization of an orthonormal basis for a Hilbert space that is important in many aspects of signal processing. Given a vector bundle equipped with a Euclidean structure, on can ask for a collection of sections that pointwise form an equal norm Parseval frame. Unlike the single vector space setting, the topology of the bundle can obstruct the existence of such families of sections. In recent work with F. Karabatman, T. Needham, and C. Shonkwiler, we have been able to identify the topological obstructions to finding such families and show they can always be constructed provided these obstructions vanish.