#harmonic analysis
12 papers match
Umbrella theorems for time-frequency representations
Paolo Boggiatto, Chiara Boiti, Alessandro Oliaro
The paper studies Umbrella Theorems—uncertainty principles that forbid a single square‑integrable function from dominating an infinite orthonormal family and its Fourier transforms…
Lebesgue measure of distance sets with regular pins and multi-scale Mizohata-Takeuchi-type estimates
Bochen Liu
The paper proves that for planar Borel sets with Hausdorff dimensions exceeding certain thresholds, there exists a point in one set whose pinned distance set has positive Lebesgue…
A construction of Kakeya Sets in Arbitrary Dimension
Rafael J. Fernández-Delgado, Mikael de la Salle
The paper presents a new method for building Kakeya sets in any dimension, achieving very small volume for their δ‑neighbourhoods and exploring implications for Fourier multiplier…
Scattering and a Plancherel formula for real reductive spherical spaces
Patrick Delorme
The paper proves a scattering theorem and a Plancherel formula for real homogeneous spherical varieties, extending results of Sakellaridis–Venkatesh to the real case using Harish‑C…
The exact -norm supremum of Walsh--Kaczmarz--Fejér kernels
István Blahota
The paper determines the exact L1‑norm supremum of Fejér kernels for the Walsh–Kaczmarz system, proving a limit of 4/3 for dyadic indices and a global supremum of 71/50.
Prime Fourier Embeddings: A Principled Basis for Modular Arithmetic
Hyunsang Hwang, Suhyun Bae, Donghun Lee
The paper proposes Prime Fourier Embeddings, a sinusoidal encoding of integers based on prime indices that makes modular arithmetic operations explicit, and shows theoretically tha…
Sharp higher order regularity of discrete maximal functions
Sung-Yi Liao, José Madrid, Eyvindur Palsson +1
The paper obtains sharp ℓ^p(Z) bounds for the first and second discrete derivatives of the uncentered Hardy‑Littlewood maximal operator applied to binary functions on the integers,…
Pulsation harmonics reveal the origin of the century-old Blazhko effect
Jia-Shu Niu
The study analyzes Kepler short‑cadence data of the RR Lyrae star V783 Cyg and finds a set of ‘disharmonized’ pulsation harmonics whose amplitudes vary opposite to the fundamental…
Harmonic Analysis on Graphs via Isometric Group Embedding: A Canonical Fourier Transform, Shift, and Convolution for Network Signals
Rigobert Fokam Souop, Laurent Bitjoka
The paper proposes a new harmonic analysis framework for graph signals by embedding a graph isometrically into a Cayley graph of a finite abelian group, enabling a canonical Fourie…
Local spectral density and Slepian concentration for spherical Fourier-Bessel truncation spaces
Xinpeng Huang
The paper studies the asymptotic behavior of diagonal kernels and eigenvalue concentrations for spherical Fourier‑Bessel truncation spaces, deriving a local density profile and a S…
Logarithmic Depletion of Vortex Stretching and Singularity Evasion in the 3D Navier-Stokes Equations
Zoran Grujic
The paper shows that for certain critical vortex configurations in the 3D incompressible Navier‑Stokes equations, a logarithmically weighted BMO condition on the vorticity directio…
Fractal uncertainty principle over
Valentino Badalucco, Leonardo Franchi
The paper establishes a fractal uncertainty principle for porous subsets of the p‑adic field \(\mathbb{Q}_p\), confirming a conjecture posed by Cohen.
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