83 citations · 515 across the 58 of their papers we have counts for
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Sampling Theorems for Shift-invariant Spaces, Gabor Frames, and Totally Positive Functions
Karlheinz Gröchenig, José Luis Romero, Joachim Stöckler
We study nonuniform sampling in shift-invariant spaces and the construction of Gabor frames with respect to the class of totally positive functions whose Fourier transform factors…
A Guide to Localized Frames and Applications to Galerkin-like Representations of Operators
Peter Balazs, Karlheinz Gröchenig
This chapter offers a detailed survey on intrinsically localized frames and the corresponding matrix representation of operators. We re-investigate the properties of localized fram…
The Cramer-Wold theorem on quadratic surfaces and Heisenberg uniqueness pairs
Karlheinz Gröchenig, Philippe Jaming
Two measurable sets form a Heisenberg uniqueness pair, if every bounded measure with support in S whose Fourier transform vanishes on Λ must be ze…
Density of Sampling and Interpolation in Reproducing Kernel Hilbert Spaces
Hartmut Führ, Karlheinz Gröchenig, Antti Haimi +2
We derive necessary density conditions for sampling and for interpolation in general reproducing kernel Hilbert spaces satisfying some natural conditions on the geometry of the spa…