Asymptotic nodal length and log-integrability of toral eigenfunctions
DOI10.1007/s00220-023-04752-3zbMath1528.42012arXiv2101.06985OpenAlexW3123903642MaRDI QIDQ6116795
Publication date: 16 August 2023
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2101.06985
Fourier transformsexponential polynomialMorgan's theoremuncertainty principle in harmonic analysislacunary trigonometric series
Estimates of eigenvalues in context of PDEs (35P15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Lacunary series of trigonometric and other functions; Riesz products (42A55) Trigonometric polynomials, inequalities, extremal problems (42A05)
Cites Work
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- Non-universality of nodal length distribution for arithmetic random waves
- On the number of nodal domains of toral eigenfunctions
- On toral eigenfunctions and the random wave model
- On probability measures arising from lattice points on circles
- Fluctuations of the nodal length of random spherical harmonics
- Nodal sets of eigenfunctions on Riemannian manifolds
- Eigenfunctions and nodal sets
- Über Knoten von Eigenfunktionen des Laplace-Beltrami-Operators
- On the angular distribution of Gaussian integers with fixed norm
- Nodal sets of Laplace eigenfunctions: polynomial upper estimates of the Hausdorff measure
- Nodal sets of Laplace eigenfunctions: proof of Nadirashvili's conjecture and of the lower bound in Yau's conjecture
- Nodal length fluctuations for arithmetic random waves
- Planck-scale distribution of nodal length of arithmetic random waves
- Nodal set of monochromatic waves satisfying the random wave model
- Boundary effect on the nodal length for arithmetic random waves, and spectral semi-correlations
- Planck-scale number of nodal domains for toral eigenfunctions
- Nodal sets and growth exponents of Laplace eigenfunctions on surfaces
- On the volume of nodal sets for eigenfunctions of the Laplacian on the torus
- Asymptotic Laws for the Spatial Distribution and the Number of Connected Components of Zero Sets of Gaussian Random Functions
- Eigenfunctions of the Laplacian on a Riemannian Manifold
- Level Sets and Extrema of Random Processes and Fields
- Regular and irregular semiclassical wavefunctions
- Nodal Sets of Laplace Eigenfunctions: Estimates of the Hausdorff Measure in Dimensions Two and Three
- On the fractal structure of attainable probability measures
- Lecture notes on quantitative unique continuation for solutions of second order elliptic equations
- Spectral Quasi Correlations and Phase Transitions for the Nodal Length of Arithmetic Random Waves
- A Problem on Sums of Two Squares
