K. Gröchenig

activity

20042026

most citedGabor Frames and Totally Positive Functions

83 citations · 515 across the 58 of their papers we have counts for

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Showing 2011Show all

3 papers · 1 filter

math.FA2011

Approximation of Fourier Integral Operators by Gabor multipliers

Elena Cordero, Karlheinz Gröchenig, Fabio Nicola

A general principle says that the matrix of a Fourier integral operator with respect to wave packets is concentrated near the curve of propagation. We prove a precise version of th…

math.FA2011★ 83 cited

Gabor Frames and Totally Positive Functions

Karlheinz Gröchenig, Joachim Stöckler

Let $g$ be a totally positive function of finite type. Then the Gabor set ${e^{2 π i β l t} g (t - α k), k, l \in Z}$ is a frame for $L^{2} (R)$ , if and only if $α β < 1$ . This result is a fi…

math.FA2011★ 21 cited

Phase Space Localization of Riesz bases for L^2(R^d)

Karlheinz Gröchenig, Eugenia Malinnikova

We prove a strong uncertainty principle for Riesz bases in L^2(R^d) and show that the orthonormal basis constructed by Bourgain possesses the optimal phase-space localization.