Gabor frames without inequalities
Abstract
We prove fourteen equivalent conditions for a set of timefrequency shifts on a lattice to be a frame for L2. Remarkably, several of these conditions can be formulated without an inequality. In particular, instead of checking the invertibility of the frame operator on L2 it suffices to verify that it is one-to-one on a certain subspace of tempered distributions.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.