43 citations · 83 across the 21 of their papers we have counts for
21 papers · 1 filter
Energy Propagation in Scattering Convolution Networks Can Be Arbitrarily Slow
Hartmut Führ, Max Getter
We analyze energy decay for deep convolutional neural networks employed as feature extractors, including Mallat's wavelet scattering transform. For time-frequency scattering transf…
Dilational Symmetries of Decomposition and Coorbit Spaces
Hartmut Führ, Reihaneh Raisi Tousi
We investigate the invariance properties of general wavelet coorbit spaces and Besov-type decomposition spaces under dilations by matrices. We show that these matrices can be chara…
The metaplectic action on modulation spaces
Hartmut Führ, Irina Shafkulovska
We study the mapping properties of metaplectic operators on modulation spaces of the type . Our main r…
Embeddings of anisotropic Besov spaces into Sobolev spaces
David Bartusel, Hartmut Führ
We study the embeddings of (homogeneous and inhomogeneous) anisotropic Besov spaces associated to an expansive matrix into Sobolev spaces, with focus on the influence of on…
Classifying decomposition and wavelet coorbit spaces using coarse geometry
Hartmut Führ, René Koch
This paper is concerned with the study of Besov-type decomposition spaces, which are scales of spaces associated to suitably defined coverings of the euclidean space …
Embeddings of shearlet coorbit spaces into Sobolev spaces
Hartmut Führ, René Koch
We investigate the existence of embeddings of shearlet coorbit spaces associated to weighted mixed -spaces into classical Sobolev spaces in dimension three by using the descri…
System bandwidth and the existence of generalized shift-invariant frames
Hartmut Führ, Jakob Lemvig
We consider the question whether, given a countable system of lattices in a locally compact abelian group , there exists a sequence of functions $(g_j)_{j \in…
A classification of continuous wavelet transforms in dimension three
Bradley Currey, Hartmut Führ, Vignon Oussa
This paper presents a full catalogue, up to conjugacy and subgroups of finite index, of all matrix groups that give rise to a continuous wavelet transf…
A classification of anisotropic Besov spaces
Jahangir Cheshmavar, Hartmut Führ
We study (homogeneous and inhomogeneous) anisotropic Besov spaces associated to expansive dilation matrices , with the goal of clarifying when two suc…
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…
Recent Progress in Shearlet Theory: Systematic Construction of Shearlet Dilation Groups, Characterization of Wavefront Sets, and New Embeddings
Giovanni S. Alberti, Stephan Dahlke, Filippo De Mari +2
The class of generalized shearlet dilation groups has recently been developed to allow the unified treatment of various shearlet groups and associated shearlet transforms that had…
Geometric Space-Frequency Analysis on Manifolds
Hans G. Feichtinger, Hartmut Führ, Isaac Z. Pesenson
This paper gives a survey of methods for the construction of space-frequency concentrated frames on Riemannian manifolds with bounded curvature, and the applications of these frame…
Wavelet Riesz bases associated to nonisotropic dilations
Hartmut Führ, Yannic Maus
A bounded, Riemann integrable and measurable set , which fulfills \[\sum\limits_{γ\inΓ}\mathbb{1}_K(x-γ)=k\text{ almost everywhere, }\] for…
Resolution of the wavefront set using general continuous wavelet transforms
Jonathan Fell, Hartmut Führ, Felix Voigtlaender
We consider the problem of characterizing the wavefront set of a tempered distribution in terms of its continuous wavelet transform, where the la…
Relevant sampling in finitely generated shift-invariant spaces
Hartmut Führ, Jun Xian
We consider random sampling in finitely generated shift-invariant spaces generated by a vector $Φ= (φ_1,\ldots,φ_r) \in {\rm L}^2(\mathbb{R}^…
Simplified vanishing moment criteria for wavelets over general dilation groups, with applications to abelian and shearlet dilation groups
Hartmut Führ, Reihaneh Raisi Tousi
We consider the coorbit theory associated to general continuous wavelet transforms arising from a square-integrable, irreducible quasi-regular representation of a semidirect produc…
Wavelet Coorbit Spaces viewed as Decomposition Spaces
Hartmut Führ, Felix Voigtlaender
In this paper we show that the Fourier transform induces an isomorphism between the coorbit spaces defined by Feichtinger and Gröchenig of the mixed, weighted Lebesgue spaces $L_{v…
Coorbit spaces and wavelet coefficient decay over general dilation groups
Hartmut Führ
We study continuous wavelet transforms associated to matrix dilation groups giving rise to an irreducible square-integrable quasi-regular representation on ${\rm L}^2(\mathbb{R}^d)…
Poincaré and plancherel-polya inequalities in harmonic analysis on weighted combinatorial graphs
Hartmut F"uhr, Isaac Z. Pesenson
We prove Poincaré and Plancherel-Polya inequalities for weighted {\ell}p -spaces on weighted graphs in which the constants are explicitly expressed in terms of some geometric chara…
Homogeneous Besov spaces on stratified Lie groups and their wavelet characterization
Hartmut Führ, Azita Mayeli
We establish wavelet characterizations of homogeneous Besov spaces on stratified Lie groups, both in terms of continuous and discrete wavelet systems. We first introduce a notion o…
The weak Paley-Wiener property for group extensions
Hartmut Fuehr
The paper studies weak Paley-Wiener properties for group extensions by use of Mackey's theory. The main theorem establishes sufficient conditions on the dual action to ensure that…