15 citations · 37 across the 10 of their papers we have counts for
11 papers
The Lifting Property for Frame Multipliers and Toeplitz Operators
Peter Balazs, Karlheinz Gröchenig
Frame multipliers are an abstract version of Toeplitz operators in frame theory and consist of a composition of a multiplication operator with the analysis and synthesis operators.…
More Uncertainty Principles for Metaplectic Time-Frequency Representations
Karlheinz Gröchenig, Irina Shafkulovska
We develop a method for the transfer of an uncertainty principle for the short-time Fourier transform or a Fourier pair to an uncertainty principle for a sesquilinear or quadratic…
Hölder-Continuity of Extreme Spectral Values of Pseudodifferential Operators, Gabor Frame Bounds, and Saturation
Karlheinz Gröchenig, José Luis Romero, Michael Speckbacher
We build on our recent results on the Lipschitz dependence of the extreme spectral values of one-parameter families of pseudodifferential operators with symbols in a weighted Sjöst…
Spectral Invariance of Quasi-Banach Algebras for Matrices and Pseudodifferential Operators
Karlheinz Gröchenig, Christine Pfeuffer, Joachim Toft
In the paper we extend the spectral invariance of pseudodifferential operators acting on (non-weighted) classical modulation spaces to allow the Lebesgue exponents to be smaller th…
Balian-Low type theorems on homogeneous groups
Karlheinz Gröchenig, José Luis Romero, David Rottensteiner +1
We prove strict necessary density conditions for coherent frames and Riesz sequences on homogeneous groups. Let be a connected, simply connected nilpotent Lie group with a dila…
Kernel Theorems in Coorbit Theory
Peter Balazs, Karlheinz Gröchenig, Michael Speckbacher
We prove general kernel theorems for operators acting between coorbit spaces. These are Banach spaces associated to an integrable representation of a locally compact group and cont…
Strict density inequalities for sampling and interpolation in weighted spaces of holomorphic functions
Karlheinz Gröchenig, Antti Haimi, Joaquim Ortega-Cerdà +1
Answering a question of Lindholm, we prove strict density inequalities for sampling and interpolation in Fock spaces of entire functions in several complex variables defined by a p…
Gabor Frames: Characterizations and Coarse Structure
Karlheinz Gröchenig, Sarah Koppensteiner
This survey offers a systematic and streamlined exposition of the most important characterizations of Gabor frames over a lattice. The goal is to collect the most important charact…
Partitions of Unity and New Obstructions for Gabor Frames
Karlheinz Gröchenig
We derive new obstructions for Gabor frames. This note explains and proves the computer generated observations of Lemvig and Nielsen in arXiv:1507.03982.
New atomic decompositons for Bergman spaces on the unit ball
Jens Christensen, Karlheinz Gröchenig, Gestur Ólafsson
We derive atomic decompositions and frames for weighted Bergman spaces of several complex variables on the unit ball in the spirit of Coifman, Rochberg, and Luecking. In contrast t…
Compactness Criteria in Function Spaces
Monika Dörfler, Hans G. Feichtinger, Karlheinz Gröchenig
The classical criterion for compactness in Banach spaces of functions can be reformulated into a simple tightness condition in the time-frequency domain. This description preserves…