Götz E. Pfander
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Prony’s Method in Banach Modules Open
We show that the classical Prony’s method for recovery of a sparse signal from its consecutive Fourier coefficients can be viewed as a spectral identification problem for an unknown restriction of a known linear operator. This presents a u…
Prony's Method in Banach Modules Open
We show that the classical Prony's method for recovery of a sparse signal from its consecutive Fourier coefficients can be viewed as a spectral identification problem for an unknown restriction of a known linear operator. This presents a u…
Cube tilings with linear constraints Open
We consider tilings $(\mathcal{Q},Φ)$ of $\mathbb{R}^d$ where $\mathcal{Q}$ is the $d$-dimensional unit cube and the set of translations $Φ$ is constrained to lie in a pre-determined lattice $A \mathbb{Z}^d$ in $\mathbb{R}^d$. We provide a…
Exponential bases for parallelepipeds with frequencies lying in a prescribed lattice Open
The existence of a Fourier basis with frequencies in $\mathbb{R}^d$ for the space of square integrable functions supported on a given parallelepiped in $\mathbb{R}^d$, has been well understood since the 1950s. In a companion paper, we deri…
Bases of complex exponentials with restricted supports Open
The complex exponentials with integer frequencies form a basis for the space of square integrable functions on the unit interval. We analyze whether the basis property is maintained if the support of the complex exponentials is restricted …
Quantitative Approximation Results for Complex-Valued Neural Networks Open
Until recently, applications of neural networks in machine learning have almost exclusively relied on real-valued networks. It was recently observed, however, that complex-valued neural networks (CVNNs) exhibit superior performance in appl…
Exponential bases for partitions of intervals Open
For a partition of $[0,1]$ into intervals $I_1,\ldots,I_n$ we prove the existence of a partition of $\mathbb{Z}$ into $Λ_1,\ldots, Λ_n$ such that the complex exponential functions with frequencies in $ Λ_k$ form a Riesz basis for $L^2(I_k)…
Robust Phase Retrieval Algorithm for Time-Frequency Structured Measurements Open
We address the problem of signal reconstruction from intensity measurements with respect to a measurement frame. This non-convex inverse problem is known as phase retrieval. The case considered in this paper concerns phaseless measurements…
A Balian-Low Theorem for Subspaces Open
We extend the Balian-Low theorem to Gabor subspaces of $L^2(\mathbb R)$ by involving the concept of additional time-frequency shift invariance. We prove that if a Gabor system on a lattice of rational density is a Riesz sequence generating…
Blind Deconvolution with Additional Autocorrelations via Convex Programs Open
In this work we characterize all ambiguities of the linear (aperiodic) one-dimensional convolution on two fixed finite-dimensional complex vector spaces. It will be shown that the convolution ambiguities can be mapped one-to-one to factori…
Robust Phase Retrieval Algorithm for Time-Frequency Structured\n Measurements Open
We address the problem of signal reconstruction from intensity measurements\nwith respect to a measurement frame. This non-convex inverse problem is known\nas phase retrieval. The case considered in this paper concerns phaseless\nmeasureme…