Maximally localized Gabor orthonormal bases on locally compact abelian groups
DOI10.1016/j.aim.2024.109786MaRDI QIDQ6592202
Publication date: 24 August 2024
Published in: Advances in Mathematics (Search for Journal in Brave)
extremal functionsshort-time Fourier transformlocally compact abelian groupstime-frequency localizationGabor orthonormal basesLieb's uncertainty inequality
Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Optimization of shapes other than minimal surfaces (49Q10) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25)
Cites Work
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- Time-frequency analysis on the adeles over the rationals
- Fourier transforms of finite chirps
- Uncertainty in time-frequency representations on finite Abelian groups and applications
- Metaplectic operators for finite Abelian groups and \(\mathbb R^d\)
- Gabor analysis over finite Abelian groups
- Differentiation and the Balian-Low theorem
- Hermite functions and uncertainty principles for the Fourier and the windowed Fourier trans\-forms.
- Beweis des Ergodensatzes und des \(H\)-Theorems in der neuen Mechanik.
- Foundations of time-frequency analysis
- Localization operators and an uncertainty principle for the discrete short time Fourier transform
- An uncertainty principle for cyclic groups of prime order
- Orthonormal bases in the orbit of square-integrable representations of nilpotent Lie groups
- Metaplectic groups and Segal algebras
- Multiplier representations of Abelian groups
- The uniformity of non-uniform Gabor bases
- Phase space localization of Riesz bases for \(L^2(\mathbb{R}^d)\)
- On the construction of discrete orthonormal Gabor bases on finite dimensional spaces
- Donoho-Logan large sieve principles for modulation and polyanalytic Fock spaces
- Wehrl-type coherent state entropy inequalities for \(\mathrm{SU}(1,1)\) and its \(AX+B\) subgroup
- Gabor orthonormal bases, tiling and periodicity
- Deformations and Balian-Low theorems for Gabor frames on the adeles
- On the existence of optimizers for time-frequency concentration problems
- A fractal uncertainty principle for the short-time Fourier transform and Gabor multipliers
- Uncertainty principle via variational calculus on modulation spaces
- Functionals with extrema at reproducing kernels
- The Faber-Krahn inequality for the short-time Fourier transform
- A note on the HRT conjecture and a new uncertainty principle for the short-time Fourier transform
- Tiling functions and Gabor orthonormal basis
- Non-separable lattices, Gabor orthonormal bases and tilings
- Gabor orthonormal bases generated by the unit cubes
- Uniformity of measures with Fourier frames
- Harmonic analysis and theta-functions
- Sur certains groupes d'opérateurs unitaires
- The uncertainty principle for the short-time Fourier transform on finite cyclic groups: cases of equality
- Uncertainty Principles and Signal Recovery
- The uncertainty principle
- The Uncertainty Principle on Groups
- Integral bounds for radar ambiguity functions and Wigner distributions
- Sharpness in Young’s inequality for convolution
- Zeros of the Zak transform on locally compact abelian groups
- A note on Gabor orthonormal bases
- On Gabor orthonormal bases over finite prime fields
- Equality cases for the uncertainty principle in finite Abelian groups
- METAPLECTIC OPERATORS ON Cn
- Pseudodifferential operators on locally compact abelian groups and Sjöstrand's symbol class
- The uncertainty principle: Variations on a theme
- A characterization for windowed Fourier orthonormal basis with compact support
- Contraction property of certain classes of log-\(\mathcal{M}\)-subharmonic functions in the unit ball
- A Faber–Krahn inequality for Wavelet transforms
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