Frames, the frame operator, and dual frames

Keri Kornelson, University of Oklahoma

3:30 pm - 4:30 pm, PHSC 1105

This talk will explore frames in finite dimensions. A frame can be thought of as a generalization of a basis. We retain the spanning property of a basis, but do not require unique reconstruction coefficients. In finite dimensions, every spanning set is a frame. We present the key operators associated to a frame, the analysis, synthesis, and frame operators. Properties of a frame are embedded in these operators. From the frame operator for a frame F, we are able to define a dual frame G. These dual frames act together to create an orthonormal-basis-like reconstruction property.
(Joint with the Analysis and Convexity Seminar)