83 citations · 515 across the 58 of their papers we have counts for
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Spectral Subspaces of Sturm-Liouville Operators and Variable Bandwidth
Mark Jason Celiz, Karlheinz Gröchenig, Andreas Klotz
We study spectral subspaces of the Sturm-Liouville operator on , where is a positive, piecewise constant function. Functions in these subspaces…
Sampling the flow of a bandlimited function
Akram Aldroubi, Karlheinz Gröchenig, Longxiu Huang +3
We analyze the problem of reconstruction of a bandlimited function from the space-time samples of its states resulting from the convolution with a kernel .…
Zeros of the Wigner Distribution and the Short-Time Fourier Transform
Karlheinz Gröchenig, Philippe Jaming, Eugenia Malinnikova
We study the question under which conditions the zero set of a (cross-) Wigner distribution W (f, g) or a short-time Fourier transform is empty. This is the case when both f and g…
Sharp results on sampling with derivatives in shift-invariant spaces and multi-window Gabor frames
Karlheinz Gröchenig, José Luis Romero, Joachim Stöckler
We study the problem of sampling with derivatives in shift-invariant spaces generated by totally-positive functions of Gaussian type or by the hyperbolic secant. We provide sharp c…
From Heisenberg uniqueness pairs to properties of the Helmholtz and Laplace equations
Aingeru Fernandez-Bertolin, Karlheinz Gröchenig, Philippe Jaming
The aim of this paper is to establish uniqueness properties of solutions of the Helmholtz and Laplace equations. In particular, we show that if two solutions of such equations on a…
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…