The problem of imaging point objects can be formulated as estimation of an unknown atomic
measure from its M+ 1 consecutive noisy Fourier coefficients. The standard resolution of this …

For quantum systems with a finite dimensional Hilbert space of states, we show that the
complete incompatibility of two observables—a notion we introduce—is equivalent to the …

Kirkwood-Dirac (KD) distribution is a representation of quantum states. Recently, KD
distribution has been found applications in many areas such as in quantum metrology …

Gabor frames have been extensively studied in time-frequency analysis over the last 30
years. They are commonly used in science and engineering to synthesize signals from, or to …

For two orthonormal bases of ad-dimensional complex Hilbert space, the notion of complete
incompatibility was introduced recently by De Bièvre,[Phys. Rev. Lett. 127, 190404 (2021)] …

Group equivariant convolutional neural networks (G-CNNs) are generalizations of
convolutional neural networks (CNNs) which excel in a wide range of technical applications …

We introduce the notion of finite right (or left) numerical index on a C∗-bimodule AXB with a
bi-Hilbertian structure, based on a Pimsner–Popa-type inequality. The right index of X can …

A well-known version of the uncertainty principle on the cyclic group ZN states that for any
couple of functions f, g∈ ℓ 2 (ZN)∖{0}, the short-time Fourier transform V gf has support of …

As a time‐shifted and frequency‐modulated version of the linear canonical transform (LCT),
the offset linear canonical transform (OLCT) provides a more general framework of most …

Classical and recent results on uncertainty principles for functions on finite Abelian groups
relate the cardinality of the support of a function to the cardinality of the support of its Fourier …