Nir Lev - Research Publications

My research is in Harmonic Analysis and related topics such as:

Most of the papers below are also available in arXiv version.

  1. Completeness of sparse, almost integer and finite local complexity sequences of translates in L^p(R) (with A. Tselishchev). Submitted.
  2. Schauder frames of discrete translates in L^p(R) (with A. Tselishchev). Submitted.
  3. Schauder frames of discrete translates in L^2(R) (with A. Tselishchev). Submitted.
  4. Maximality and completeness of orthogonal exponentials on the cube (with M. Kolountzakis, M. Matolcsi). Expositiones Mathematicae. Accepted.
  5. Completeness of uniformly discrete translates in L^p(R). Journal d'Analyse Mathématique (2025).
  6. Support of extremal doubly stochastic arrays (with M. Etkind). Israel Journal of Mathematics (2025).
  7. There are no unconditional Schauder frames of translates in L^p(R), 1≤p≤2 (with A. Tselishchev). Advances in Mathematics 460 (2025), Paper No. 110036, 11 pp.
  8. Functions tiling simultaneously with two arithmetic progressions (with M. Etkind). Proceedings of the London Mathematical Society 127 (2023), no. 6, 1775-1815.
  9. Spectral sets and weak tiling (with M. Kolountzakis, M. Matolcsi). Sampling Theory, Signal Processing, and Data Analysis 21 (2023), Paper No. 31, 21 pp.
  10. The Fuglede conjecture for convex domains is true in all dimensions (with M. Matolcsi). Acta Mathematica 228 (2022), no. 2, 385-420.
  11. Gabor orthonormal bases, tiling and periodicity (with A. Debernardi). Mathematische Annalen 384 (2022), no. 3-4, 1461-1467.
  12. Riesz bases of exponentials for convex polytopes with symmetric faces (with A. Debernardi). Journal of the European Mathematical Society JEMS 24 (2022), no. 8, 3017-3029.
  13. An example concerning Fourier analytic criteria for translational tiling. Revista Matemática Iberoamericana 38 (2022), no. 6, 1975-1991.
  14. Tiling by translates of a function: results and open problems (with M. Kolountzakis). Discrete Analysis 2021, Paper No. 12, 24 pp.
  15. Spectrality of polytopes and equidecomposability by translations (with B. Liu). International Mathematics Research Notices IMRN 2021, no. 18, 13867-13891.
  16. Crystalline temperate distributions with uniformly discrete support and spectrum (with G. Reti). Journal of Functional Analysis 281 (2021), no. 4, Paper No. 109072, 15 pp.
  17. Poisson summation formulas involving the sum-of-squares function (with G. Reti). Israel Journal of Mathematics 246 (2021), no. 1, 403-421.
  18. Spectrality of product domains and Fuglede's conjecture for convex polytopes (with R. Greenfeld). Journal d'Analyse Mathématique 140 (2020), no. 2, 409-441.
  19. Multi-tiling and equidecomposability of polytopes by lattice translates (with B. Liu). Bulletin of the London Mathematical Society 51 (2019), no. 6, 1079-1098.
  20. Fourier frames for singular measures and pure type phenomena. Proceedings of the American Mathematical Society 146 (2018), no. 7, 2883-2896.
  21. Riesz bases, Meyer's quasicrystals, and bounded remainder sets (with S. Grepstad). Transactions of the American Mathematical Society 370 (2018), no. 6, 4273-4298.
  22. Fuglede's spectral set conjecture for convex polytopes (with R. Greenfeld). Analysis & PDE 10 (2017), no. 6, 1497-1538.
  23. Fourier quasicrystals and discreteness of the diffraction spectrum (with A. Olevskii). Advances in Mathematics 315 (2017), 1-26.
  24. Quasicrystals with discrete support and spectrum (with A. Olevskii). Revista Matemática Iberoamericana 32 (2016), no. 4, 1341-1352.
  25. Spectrality and tiling by cylindric domains (with R. Greenfeld). Journal of Functional Analysis 271 (2016), no. 10, 2808-2821.
  26. On non-periodic tilings of the real line by a function (with M. Kolountzakis). International Mathematics Research Notices IMRN 2016, no. 15, 4588-4601.
  27. Equidistribution estimates for Fekete points on complex manifolds (with J. Ortega-Cerdà). Journal of the European Mathematical Society JEMS 18 (2016), no. 2, 425-464.
  28. Quasicrystals and Poisson's summation formula (with A. Olevskii). Inventiones mathematicae 200 (2015), no. 2, 585-606.
  29. Separating signal from noise (with R. Peled, Y. Peres). Proceedings of the London Mathematical Society 110 (2015), no. 4, 883-931.
  30. Sets of bounded discrepancy for multi-dimensional irrational rotation (with S. Grepstad). Geometric And Functional Analysis GAFA 25 (2015), no. 1, 87-133.
  31. Universal sampling, quasicrystals and bounded remainder sets (with S. Grepstad). Comptes Rendus Mathématique 352 (2014), no. 7-8, 633-638.
  32. Multi-tiling and Riesz bases (with S. Grepstad). Advances in Mathematics 252 (2014), 1-6.
  33. Algebraic functions in the Wiener algebra (with A. Fehm, E. Paran). Communications in Algebra 42 (2014), no. 9, 3969-3979.
  34. Measures with uniformly discrete support and spectrum (with A. Olevskii). Comptes Rendus Mathématique 351 (2013), no. 15-16, 599-603.
  35. Riesz bases of exponentials on multiband spectra. Proceedings of the American Mathematical Society 140 (2012), no. 9, 3127-3132.
  36. Exponential Riesz bases, discrepancy of irrational rotations and BMO (with G. Kozma). Journal of Fourier Analysis and Applications 17 (2011), no. 5, 879-898.
  37. Uniqueness theorems for Fourier transforms. Bulletin des Sciences Mathématiques 135 (2011), no. 2, 134-140.
  38. Wiener's 'closure of translates' problem and Piatetski-Shapiro's uniqueness phenomenon (with A. Olevskii). Annals of Mathematics 174 (2011), no. 1, 519-541.
  39. No characterization of generators in l^p (1<p<2) by zero set of Fourier transform (with A. Olevskii). Comptes Rendus Mathématique 346 (2008), no. 11-12, 645-648.
  40. Piatetski-Shapiro phenomenon in the uniqueness problem (with A. Olevskii). Comptes Rendus Mathématique 340 (2005), no. 11, 793-798.

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