The Density Theorem and the Homogeneous Approximation Property for Gabor Frames

摘要: The Density Theorem for Gabor frames is a fundamental result in time-frequency analysis. Beginning with Baggett’s proof that rectangular lattice system {e2πiβntg(t − αk)}n,k∈Z must be incomplete L2(R) whenever αβ > 1, the necessary conditions to complete, frame, Riesz basis, or sequence have been extended arbitrary lattices and beyond. first partial proofs of irregular were given by Landau 1993 Ramanathan Steger 1995. A key fact proved possess certain Homogeneous Approximation Property (HAP), consequence this HAP. This chapter provides brief history detailed account Steger. Furthermore, we show techniques can used give full general version higher dimensions finitely many generators.