resented in this document is work leading to a mathematical frame tailored to speech processing. This development is based on work in three loosely-connected areas of mathematics.;The first area involves Carleson inequalities and representations in the Hardy spaces, ;The second area involves mathematical frames. A frame for ;The third area, closely related to the first, concerns developing frames for the Hilbert space, ;The results from these three areas are combined to create a class of frames for... |