26 citations · 63 across the 31 of their papers we have counts for
34 papers
Optimal concentration in the Paley-Wiener space
Luís Daniel Abreu, Michael Speckbacher
Let be a bounded interval and let be the corresponding Paley--Wiener space. For a measurable set of finite measure, consider the…
Spectral deviation of concentration operators on reproducing kernel Hilbert spaces
Felipe Marceca, José Luis Romero, Michael Speckbacher +1
We study the eigenvalue profile of concentration operators (multiplication by an indicator function followed by projection) acting on reproducing kernel Hilbert spaces. The spectra…
Convergence of Hermite expansions in modulation spaces
Philippe Jaming, Michael Speckbacher
The aim of this paper is to give an elementary proof that Hermite expensions of a function in the modulation space converges to in when and…
On quantum large sieve inequalities and operator recovery from incomplete information
Luís Daniel Abreu, Michael Speckbacher, Erling A. T. Svela
We obtain large sieve type inequalities for the Rayleigh quotient of the restriction of phase space representations of higher rank operators, via an operator analogue of the short-…
Localized frames without inequalities
Peter Balazs, Lukas Köhldorfer, Michael Speckbacher
We consider countable families of vectors in a separable Hilbert space, which are mutually localized with respect to a fixed localized Riesz basis. We prove the equivalence of the…
Localised frames for tensor product spaces
Dimitri Bytchenkoff, Michael Speckbacher, Peter Balazs
In this paper, we investigate whether the tensor product of two frames, each individually localised with respect to a spectral matrix algebra, is also localised with respect to a s…
How large are the gaps in phase space?
Michael Speckbacher
Given a sampling measure for the wavelet transform (resp. the short-time Fourier transform) with the wavelet (resp. window) being chosen from the family of Laguerre (resp. Hermite)…
Hölder-Continuity of Extreme Spectral Values of Pseudodifferential Operators, Gabor Frame Bounds, and Saturation
Karlheinz Gröchenig, José Luis Romero, Michael Speckbacher
We build on our recent results on the Lipschitz dependence of the extreme spectral values of one-parameter families of pseudodifferential operators with symbols in a weighted Sjöst…
Kernel theorems for operators on co-orbit spaces associated with localised frames
Dimitri Bytchenkoff, Michael Speckbacher, Peter Balazs
Kernel theorems, in general, provide a convenient representation of bounded linear operators. For the operator acting on a concrete function space, this means that its action on an…
Oversampling and Donoho-Logan type theorems in model spaces
Anton Baranov, Philippe Jaming, Karim Kellay +1
The aim of this paper is to extend two results from the Paley--Wiener setting to more generalmodel spaces. The first one is an analogue of the oversampling Shannon sampling formula…
Eigenvalue estimates for Fourier concentration operators on two domains
Felipe Marceca, José Luis Romero, Michael Speckbacher
We study concentration operators associated with either the discrete or the continuous Fourier transform, that is, operators that incorporate a spatial cut-off and a subsequent fre…
Comment on 'Comment on 'Affine density, von Neumann dimension and a problem of Perelomov"
Luís Daniel Abreu
In the Letter 'Comment on 'Affine density, von Neumann dimension and a problem of Perelomov', arXiv.2211.04879, by Prof. J. L. Romero, it is claimed that the main theorem of Ref2 :…
Quantitative bounds for unconditional pairs of frames
Peter Balazs, Daniel Freeman, Roxana Popescu +1
We formulate a quantitative finite-dimensional conjecture about frame multipliers and prove that it is equivalent to Conjecture 1 in [SB2]. We then present solutions to the conject…
Donoho-Logan large sieve principles for the wavelet transform
Luís Daniel Abreu, Michael Speckbacher
In this paper we formulate Donoho and Logan's large sieve principle for the wavelet transform on the Hardy space, adapting the concept of maximum Nyquist density to the hyperbolic…
Time-frequency analysis on flat tori and Gabor frames in finite dimensions
Luis Daniel Abreu, Peter Balazs, Nicki Holighaus +2
We provide the foundations of a Hilbert space theory for the short-time Fourier transform (STFT) where the flat tori \begin{equation*} \mathbb{T}_{N}^2=\mathbb{R}^2/(\mathbb{Z}\tim…
Lipschitz Continuity of Spectra of Pseudodifferential Operators in a Weighted Sjöstrand Class and Gabor Frame Bounds
Karlheinz Gröchenig, José Luis Romero, Michael Speckbacher
We study one-parameter families of pseudodifferential operators whose Weyl symbols are obtained by dilation and a smooth deformation of a symbol in a weighted Sjöstrand class. We s…
Estimation of binary time-frequency masks from ambient noise
José Luis Romero, Michael Speckbacher
We investigate the retrieval of a binary time-frequency mask from a few observations of filtered white ambient noise. Confirming household wisdom in acoustic modeling, we show that…
Spectral-norm risk rates for multi-taper estimation of Gaussian processes
José Luis Romero, Michael Speckbacher
We consider the estimation of the covariance of a stationary Gaussian process on a multi-dimensional grid from observations taken on a general acquisition domain. We derive spectra…
Sampling trajectories for the short-time Fourier transform
Michael Speckbacher
We study the problem of stable reconstruction of the short-time Fourier transform from samples taken from trajectories in . We first consider the interplay between relative d…
Affine density, von Neumann dimension and a problem of Perelomov
Luìs Daniel Abreu, Michael Speckbacher
We provide a solution to Perelomov's 1972 problem concerning the existence of a phase transition (known in signal analysis as 'Nyquist rate') determining the basis properties of ce…
Concentration estimates for finite expansions of spherical harmonics on two-point homogeneous spaces via the large sieve principle
Philippe Jaming, Michael Speckbacher
We study the concentration problem on compact two-point homogeneous spaces of finite expansions of eigenfunctions of the Laplace-Beltrami operator using large sieve methods. We der…
Almost Everywhere Convergence of Prolate Spheroidal Series
Philippe Jaming, Michael Speckbacher
In this paper, we show that the expansions of functions from -Paley-Wiener type spaces in terms of the prolate spheroidal wave functions converge almost everywhere for $1<p<\i…
Concentration estimates for band-limited spherical harmonics expansions via the large sieve principle
Michael Speckbacher, Tomasz Hrycak
We study a concentration problem on the unit sphere for band-limited spherical harmonics expansions using large sieve methods. We derive upper bounds for concentrati…
Planar sampling sets for the short-time Fourier transform
Philippe Jaming, Michael Speckbacher
This paper considers the problem of restricting the short-time Fourier transform to domains of nonzero measure in the plane and studies sampling bounds of such systems. In particul…