Groups of Affine Transformations, Convolution Idempotents, and Wavelet Transforms

Abstract: The classical continuous wavelet transform has a wide array of applications in harmonic analysis, function theory, and signal processing. Higher dimensional analogs, such as the shearlet transform fmd similar applications, including in image processing. In this talk, we will explore the role that the unitary representations of certain groups of affme transformations played in the discovery of many different wavelet-like transfonnations. The concept of a self-adjoint convolution idempotent will provide an intermediate step.

Mathematics

Audience: researchers in the topic

IPM-Isfahan Mathematics Colloquium