Super-resolution limit of the ESPRIT algorithm
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 …
measure from its M+ 1 consecutive noisy Fourier coefficients. The standard resolution of this …
Complete incompatibility, support uncertainty, and Kirkwood-Dirac nonclassicality
S De Bièvre - Physical Review Letters, 2021 - APS
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 …
complete incompatibility of two observables—a notion we introduce—is equivalent to the …
[HTML][HTML] Kirkwood-Dirac classical pure states
J Xu - Physics Letters A, 2024 - Elsevier
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 …
distribution has been found applications in many areas such as in quantum metrology …
Gabor frames in finite dimensions
GE Pfander - Finite Frames: Theory and Applications, 2013 - Springer
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 …
years. They are commonly used in science and engineering to synthesize signals from, or to …
Classification of incompatibility for two orthonormal bases
J Xu - Physical Review A, 2022 - APS
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)] …
incompatibility was introduced recently by De Bièvre,[Phys. Rev. Lett. 127, 190404 (2021)] …
Implicit bias of linear equivariant networks
Group equivariant convolutional neural networks (G-CNNs) are generalizations of
convolutional neural networks (CNNs) which excel in a wide range of technical applications …
convolutional neural networks (CNNs) which excel in a wide range of technical applications …
Jones index theory for Hilbert C∗-bimodules and its equivalence with conjugation theory
T Kajiwara, C Pinzari, Y Watatani - Journal of Functional Analysis, 2004 - Elsevier
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 …
bi-Hilbertian structure, based on a Pimsner–Popa-type inequality. The right index of X can …
[HTML][HTML] The uncertainty principle for the short-time Fourier transform on finite cyclic groups: cases of equality
F Nicola - Journal of Functional Analysis, 2023 - Elsevier
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 …
couple of functions f, g∈ ℓ 2 (ZN)∖{0}, the short-time Fourier transform V gf has support of …
Uncertainty principles associated with the offset linear canonical transform
H Huo, W Sun, L Xiao - Mathematical Methods in the Applied …, 2019 - Wiley Online Library
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 …
the offset linear canonical transform (OLCT) provides a more general framework of most …
Uncertainty in time–frequency representations on finite Abelian groups and applications
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 …
relate the cardinality of the support of a function to the cardinality of the support of its Fourier …