43 citations · 71 across the 9 of their papers we have counts for
12 papers
Quantitative estimates: How well does the discrete Fourier transform approximate the Fourier transform on
Martin Ehler, Karlheinz Gröchenig, Andreas Klotz
In order to compute the Fourier transform of a function on the real line numerically, one samples on a grid and then takes the discrete Fourier transform. We derive exact e…
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…
Necessary Density Conditions for Sampling and Interpolation in Spectral Subspaces of Elliptic Differential Operators
Karlheinz Gröchenig, Andreas Klotz
We prove necessary density conditions for sampling in spectral subspaces of a second order uniformly elliptic differential operator on with slowly oscillating symbol. For con…
Phase Transitions in Rate Distortion Theory and Deep Learning
Philipp Grohs, Andreas Klotz, Felix Voigtlaender
Rate distortion theory is concerned with optimally encoding a given signal class using a budget of bits, as . We say that can be compres…
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…
What is Variable Bandwidth?
Karlheinz Gröchenig, Andreas Klotz
We propose a new notion of variable bandwidth that is based on the spectral subspaces of an elliptic operator where is a strictly positive function. Denote…
The Optimal Dyadic Derivative
Andreas Klotz
We show that the best approximation to the difference operators on the cyclic groups of order by a dyadic convolution operator are the restrictions of a generalized dyadic de…
Norm-Controlled Inversion in Smooth Banach Algebras, II
Karlheinz Gröchenig, Andreas Klotz
We show that smoothness implies norm-controlled inversion: the smoothness of an element in a Banach algebra with a one-parameter automorphism group is preserved under inversion…
Norm-Controlled Inversion in Smooth Banach Algebras, I
Karlheinz Gröchenig, Andreas Klotz
Every differential subalgebra of a unital -algebra is spectrally invariant. We derive a quantitative version of this well-known fact and show that a minimal amount of smoothne…
Inverse Closed Ultradifferential Subalgebras
Andreas Klotz
In previous work we have shown that classical approximation theory provides methods for the systematic construction of inverse-closed smooth subalgebras. Now we extend this work to…
Spectral Invariance of Besov-Bessel Subalgebras
Andreas Klotz
Using principles of the theory of smoothness spaces we give systematic constructions of scales of inverse-closed subalgebras of a given Banach algebra with the action of a d-parame…
Noncommutative Approximation: Inverse-Closed Subalgebras and Off-Diagonal Decay of Matrices
Karlheinz Gröchenig, Andreas Klotz
We investigate two systematic constructions of inverse-closed subalgebras of a given Banach algebra or operator algebra A, both of which are inspired by classical principles of app…