Highly efficient representation and processing of multidimensional data (smoothing, compression, etc.) is best suited using approximation spaces with highly (spatially) localized bases.
Over the past 30 years, kernel functions have proved to be quite useful in representing scattered data in Euclidean spaces and other manifolds such as spheres etc. However such kernels tend to be globally supported, leading to full, ill-conditioned interpolation and least square matrices as well as a lack of local error analysis.
This talk will focus on some recently discovered highly localized kernel bases on manifolds which overcome some of these above obstacles.