Related papers: Time-frequency shift invariance of Gabor spaces ge…
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It is noted that, in contrast to widespread believes, free fields do not only allow for global, but also for local gauge invariance.
We show that the construction of Gabor frames in $L^{2}(\mathbb{R})$ with generators in $\mathbf{S}_{0}(\mathbb{R})$ and with respect to time-frequency shifts from a rectangular lattice $\alpha\mathbb{Z}\times\beta\mathbb{Z}$ is equivalent…
In the authors' first paper, Beurling-Rudin-Korenbljum type characterization of the closed ideals in a certain algebra of holomorphic functions was used to describe the lattice of invariant subspaces of the shift plus a complex Volterra…
Given discrete groups $\Gamma \subset \Delta$ we characterize $(\Gamma,\sigma)$-invariant spaces that are also invariant under $\Delta$. This will be done in terms of subspaces that we define using an appropriate Zak transform and a…
Modifications inspired by quantum gravity in the kinematics of special relativity can manifest in various ways, including anomalies in the time of flight of massless particles and the emergence of decay channels for otherwise stable…
Invariance under translation is exploited to efficiently simulate one-dimensional quantum lattice systems in the limit of an infinite lattice. Both the computation of the ground state and the simulation of time evolution are considered.
We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and study its properties. Further, we study how the invariant measures depend on the…
We investigate the problem of constructing sparse time-frequency representations with flexible frequency resolution, studying the theory of nonstationary Gabor frames in the framework of decomposition spaces. Given a painless nonstationary…