By Gestur Olafsson, Eric L. Grinberg, David Larson, Palle E. T. Jorgensen, Peter R. Massopust

This quantity relies on precise periods held on the AMS Annual assembly in New Orleans in January 2007, and a satellite tv for pc workshop held in Baton Rouge on January 4-5, 2007. It involves invited expositions that jointly symbolize a wide spectrum of fields, stressing striking interactions and connections among components which are mostly regarded as disparate. the most themes are geometry and indispensable transforms. at the one facet are harmonic research, symmetric areas, illustration conception (the teams contain non-stop and discrete, finite and endless, compact and non-compact), operator idea, PDE, and mathematical likelihood. relocating within the utilized course we stumble upon wavelets, fractals, and engineering subject matters similar to frames and sign and snapshot processing. the themes lined during this publication shape a unified entire, they usually stand on the crossroads of natural and utilized arithmetic. The articles conceal a extensive variety in harmonic research, with the most topics relating to quintessential geometry, the Radon rework, wavelets and body theory.These subject matters can loosely be grouped jointly as follows: body thought and purposes Harmonic research and serve as areas Harmonic research and quantity thought critical Geometry and Radon Transforms Multiresolution research, Wavelets, and functions