246 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Austrian Academy of SciencesAT76 papers
- University of ViennaAT26 papers
- Centre National de la Recherche ScientifiqueFR5 papers
- UCLouvainBE4 papers
- Laboratoire des Sciences du Numérique de NantesFR3 papers
- Nantes UniversitéFR3 papers
- Princeton UniversityUS3 papers
- Technical University of DenmarkDK3 papers
- TU WienAT3 papers
- University of MaraghehIR3 papers
- University of Novi SadRS3 papers
- AIT Austrian Institute of Technology GmbHAT2 papers
47 papers · 1 filter
Homogeneous Banach spaces as Banach convolution modules over
Hans G. Feichtinger
We develop an elementary approach to convolution and Fourier analysis on a locally compact Abelian group (G), based on bounded measures and bounded uniform partitions of unity. In…
Measure-operator convolutions and applications to mixed-state Gabor multipliers
Hans G. Feichtinger, Simon Halvdansson, Franz Luef
For the Weyl-Heisenberg group, convolutions between functions and operators were defined by Werner as a part of a framework called quantum harmonic analysis. We show how recent res…
Random periodic sampling patterns for shift-invariant spaces
Jorge Antezana, Diana Carbajal, José Luis Romero
We consider multi-variate signals spanned by the integer shifts of a set of generating functions with distinct frequency profiles and the problem of reconstructing them from sample…
On the relation of the frame-related operators of fusion frame systems
Lukas Köhldorfer, Peter Balazs
Frames have been investigated frequently over the last few decades due to their valuable properties, which are desirable for various applications as well as interesting for theory.…
A Survey of Fusion Frames in Hilbert Spaces
Lukas Köhldorfer, Peter Balazs, Pete Casazza +4
Fusion frames are a very active area of research today because of their myriad of applications in pure mathematics, applied mathematics, engineering, medicine, signal and image pro…
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…
Comparisons between Fourier and STFT multipliers: the smoothing effect of the Short-time Fourier Transform
Peter Balazs, Federico Bastianoni, Elena Cordero +2
We study the connection between STFT multipliers having windows , symbols , , and the Fo…
Frame-related Sequences in Chains and Scales of Hilbert Spaces
Peter Balazs, Giorgia Bellomonte, Hessam Hosseinnezhad
Frames for Hilbert spaces are interesting for mathematicians but also important for applications e.g. in signal analysis and in physics. Both in mathematics and physics it is natur…
Continuous frames in tensor product Hilbert spaces, localization operators and density operators
Peter Balazs, Nenad Teofanov
Continuous frames and tensor products are important topics in theoretical physics. This paper combines those concepts. We derive fundamental properties of continuous frames for ten…
On compactly supported dual windows of Gabor frames
Diana T. Stoeva
The main purpose of the paper is to give a characterization of all compactly supported dual windows of a Gabor frame. As an application, we consider an iterative procedure for appr…
On near orthogonality of the Banach frames of the wave packet spaces
Dimitri Bytchenkoff
In solving scientific, engineering or pure mathematical problems one is often faced with a need to approximate the function of a given class by the linear combination of a preferab…
Multiple sampling and interpolation in weighted Fock spaces of entire functions
Luis Alberto Escudero, Antti Haimi, José Luis Romero
We characterize sampling and interpolating sets with derivatives in weighted Fock spaces on the complex plane in terms of their weighted Beurling densities.
On a characterization of Riesz bases via biorthogonal sequences
Diana T. Stoeva
It is well known that a sequence in a Hilbert space is a Riesz basis if and only if it is a complete Bessel sequence with biorthogonal sequence which is also a complete Bessel sequ…
Kernel Theorems in Coorbit Theory
Peter Balazs, Karlheinz Gröchenig, Michael Speckbacher
We prove general kernel theorems for operators acting between coorbit spaces. These are Banach spaces associated to an integrable representation of a locally compact group and cont…
Frames for the solution of operator equations in Hilbert spaces with fixed dual pairing
Peter Balazs, Helmut Harbrecht
For the solution of operator equations, Stevenson introduced a definition of frames, where a Hilbert space and its dual are {\em not} identified. This means that the Riesz isomorph…
U-cross Gram matrices and their invertibility
Peter Balazs, Mitra Shamsabadi, Ali Akbar Arefijamaal +1
The Gram matrix is defined for Bessel sequences by combining synthesis with subsequent analysis operators. If different sequences are used and an operator U is inserted we reach so…
Frame expansions of test functions, tempered distributions, and ultradistributions
Stevan Pilipović, Diana T. Stoeva
The paper is devoted to frame expansions in Fréchet spaces. First we review some results which concern series expansions in general Fréchet spaces via Fréchet and General Fréchet f…
A planar large sieve and sparsity of time-frequency representations
Luis Daniel Abreu, Michael Speckbacher
With the aim of measuring the sparsity of a real signal, Donoho and Logan introduced the concept of maximum Nyquist density, and used it to extend Bombieri's principle of the large…
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…
Reproducing pairs and Gabor systems at critical density
Michael Speckbacher, Peter Balazs
We use the concept of reproducing pairs to study Gabor systems at critical density. First, we present a generalization of the Balian-Low theorem to the reproducing pairs setting. T…
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…
On various R-duals and the duality principle
Diana T. Stoeva, Ole Christensen
The duality principle states that a Gabor system is a frame if and only if the corresponding adjoint Gabor system is a Riesz sequence. In general Hilbert spaces and without the ass…
Reproducing pairs and the continuous nonstationary Gabor transform on LCA groups
Michael Speckbacher, Peter Balazs
In this paper we introduce and investigate the concept of repro- ducing pairs as a generalization of continuous frames. Reproducing pairs yield a bounded analysis and synthesis pro…