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math.FA2007
Banach algebras of pseudodifferential operators and their almost diagonalization
Karlheinz Gröchenig, Ziemowit Rzeszotnik
We define new symbol classes for pseudodifferntial operators and investigate their pseudodifferential calculus. The symbol classes are parametrized by commutative convolution algeb…
math.FA2007
The Homogeneous Approximation Property and the Comparison Theorem for Coherent Frames
Karlheinz Gröchenig
We show that the homogeneous approximation property and the comparison theorem hold for arbitrary coherent frames. This observation answers some questions about the density of fram…
math.FA2007
Gabor frames without inequalities
Karlheinz Gröchenig
We prove fourteen equivalent conditions for a set of timefrequency shifts on a lattice to be a frame for L^2. Remarkably, several of these conditions can be formulated without an i…