Studies in Harmonic Analysis and Discrete Geometry: Tilings, Spectra and Quasicrystals

Project Information

HARMONIC

Grant agreement ID: 713927

DOI 10.3030/713927

Project closed

EC signature date 3 November 2016

Start date 1 December 2016

End date 30 November 2022

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost € 1 260 625,00

EU contribution € 1 260 625,00

Coordinated by

BAR ILAN UNIVERSITY
Israel

Publications

Peer reviewed articles (31)

Spectrality of product domains and Fuglede’s conjecture for convex polytopes

Author(s): Rachel Greenfeld, Nir Lev
Published in: Journal d'Analyse Mathématique, Issue 140/2, 2020, Page(s) 409-441, ISSN 0021-7670
Publisher: Magnes Press
DOI: 10.1007/s11854-020-0092-9

Quantitative weighted estimates for the Littlewood–Paley square function and Marcinkiewicz multipliers

Author(s): Andrei K. Lerner
Published in: Mathematical Research Letters, Issue 26/2, 2019, Page(s) 537-556, ISSN 1073-2780
Publisher: Mathematical Publishing
DOI: 10.4310/mrl.2019.v26.n2.a7

Riesz bases of exponentials for convex polytopes with symmetric faces

Author(s): Alberto Debernardi; Nir Lev
Published in: Journal of the European Mathematical Society, Issue 24/8, 2022, Page(s) 3017-3029, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/jems/1158

Multi‐tiling and equidecomposability of polytopes by lattice translates

Author(s): Nir Lev, Bochen Liu
Published in: Bulletin of the London Mathematical Society, Issue 51/6, 2019, Page(s) 1079-1098, ISSN 0024-6093
Publisher: Oxford University Press
DOI: 10.1112/blms.12297

Characterization of the three-dimensional multiple translative tiles

Author(s): Han, Mei; Sriamorn, Kirati; Yang, Qi; Zong, Chuanming
Published in: Advances in Mathematics, Issue 410, part B, Paper No. 108755,, 2022, Page(s) 27 pp., ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2022.108755

Crystalline temperate distributions with uniformly discrete support and spectrum

Author(s): Nir Lev, Gilad Reti
Published in: Journal of Functional Analysis, Issue 281/4, 2021, Page(s) 109072, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2021.109072

Periodic structure of translational multi-tilings in the plane

Author(s): Bochen Liu
Published in: Amer. J. Math., Issue 143/6, 2021, Page(s) 1841–1862, ISSN 0002-9327
Publisher: The Johns Hopkins University Press
DOI: 10.48550/arxiv.1809.03440

On separated bump conditions for Calderón-Zygmund operators

Author(s): Andrei K. Lerner
Published in: Proc. Amer. Math. Soc., Issue 150/3, 2022, Page(s) 1197–1208, ISSN 0002-9939
Publisher: American Mathematical Society
DOI: 10.48550/arxiv.2008.05866

A note on the Coifman–Fefferman and Fefferman–Stein inequalities

Author(s): Andrei K. Lerner
Published in: Arkiv för Matematik, Issue 58/2, 2020, Page(s) 357-367, ISSN 0004-2080
Publisher: Royal Swedish Academy of Sciences
DOI: 10.4310/arkiv.2020.v58.n2.a7

Hausdorff operators associated with the Opdam–Cherednik transform in Lebesgue spaces

Author(s): Shyam Swarup Mondal; Anirudha Poria
Published in: J. Pseudo-Differ. Oper. Appl., Issue 13/3, 2022, Page(s) Paper No. 31, 20 pp., ISSN 1662-9981
Publisher: Birkhaeuser Verlag AG
DOI: 10.1007/s11868-022-00462-x

The Fuglede conjecture for convex domains is true in all dimensions

Author(s): Lev, Nir; Matolcsi, Máté
Published in: Acta Mathematica, Issue 228/2, 2022, Page(s) 385-420, ISSN 0001-5962
Publisher: Royal Swedish Academy of Sciences
DOI: 10.4310/acta.2022.v228.n2.a3

Gabor orthonormal bases, tiling and periodicity

Author(s): Nir Lev; Alberto Debernardi Pinos
Published in: Mathematische Annalen, Issue 384/3-4, 2022, Page(s) 1461-1467, ISSN 0025-5831
Publisher: Springer Verlag
DOI: 10.48550/arxiv.2109.02240

Qualitative uncertainty principles for the windowed Opdam--Cherednik transform on weighted modulation spaces

Author(s): Anirudha Poria; Shyam Mondal
Published in: Math. Methods Appl. Sci., Issue 45/16, 2022, Page(s) 10424–10439, ISSN 1099-1476
Publisher: Wiley-Blackwell
DOI: 10.1002/mma.8376

Weighted Norm Inequalities for the Opdam--Cherednik Transform

Author(s): Anirudha Poria; Shyam Mondal
Published in: Internat. J. Math., Issue 33/9, 2022, Page(s) Paper No. 2250066, 21 pp., ISSN 0129-167X
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0129167x22500665

Fuglede’s spectral set conjecture for convex polytopes

Author(s): Rachel Greenfeld, Nir Lev
Published in: Analysis & PDE, Issue 10/6, 2017, Page(s) 1497-1538, ISSN 2157-5045
Publisher: Mathematical Sciences Publishers
DOI: 10.2140/apde.2017.10.1497

Fourier frames for singular measures and pure type phenomena

Author(s): Nir Lev
Published in: Proceedings of the American Mathematical Society, Issue 146/7, 2018, Page(s) 2883-2896, ISSN 0002-9939
Publisher: American Mathematical Society
DOI: 10.1090/proc/13849

A note on weighted bounds for rough singular integrals

Author(s): Andrei K. Lerner
Published in: Comptes Rendus Mathematique, Issue 356/1, 2018, Page(s) 77-80, ISSN 1631-073X
Publisher: Elsevier Masson
DOI: 10.1016/j.crma.2017.11.016

Fourier quasicrystals and discreteness of the diffraction spectrum

Author(s): Nir Lev, Alexander Olevskii
Published in: Advances in Mathematics, Issue 315, 2017, Page(s) 1-26, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2017.05.015

An L2-identity and pinned distance problem

Author(s): Bochen Liu
Published in: Geometric and Functional Analysis, Issue 29/1, 2019, Page(s) 283-294, ISSN 1016-443X
Publisher: Birkhauser Verlag
DOI: 10.1007/s00039-019-00482-8

Commutators of singular integrals revisited

Author(s): Andrei K. Lerner, Sheldy Ombrosi, Israel P. Rivera-Ríos
Published in: Bulletin of the London Mathematical Society, Issue 51/1, 2019, Page(s) 107-119, ISSN 0024-6093
Publisher: Oxford University Press
DOI: 10.1112/blms.12216

The Boas Problem on Hankel Transforms

Author(s): A. Debernardi
Published in: Journal of Fourier Analysis and Applications, Issue 25/6, 2019, Page(s) 3310-3341, ISSN 1069-5869
Publisher: Birkhaeuser
DOI: 10.1007/s00041-019-09703-y

Approximation via Hausdorff operators

Author(s): Alberto Debernardi, Elijah Liflyand
Published in: Canadian Mathematical Bulletin, 2020, Page(s) 1-18, ISSN 0008-4395
Publisher: Canadian Mathematical Society
DOI: 10.4153/s0008439520000612

Tiling by translates of a function: results and open problems

Author(s): Kolountzakis, Mihail N.; Lev, Nir
Published in: Discrete Analysis, Issue Paper No. 12, 2021, Page(s) 24 pp, ISSN 2397-3129
Publisher: Discrete Analysis
DOI: 10.48550/arxiv.2009.09410

Localization operators associated with the windowed Opdam-Cherednik transform on modulation spaces

Author(s): Anirudha Poria
Published in: Complex Variables and Elliptic Equations, 2022, ISSN 1747-6933
Publisher: Taylor & Francis
DOI: 10.1080/17476933.2022.2052861

On two weight estimates for iterated commutators

Author(s): Andrei K. Lerner; Sheldy Ombrosi; Israel P. Rivera-Ríos
Published in: J. Funct. Anal., Issue 281/8, Paper No. 109153, 2021, Page(s) 46 pp., ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2021.109153

Weighted norm inequalities for generalized Fourier-type transforms and applications

Author(s): A. Debernardi
Published in: Publicacions Matemàtiques, Issue 64, 2020, Page(s) 3-42, ISSN 0214-1493
Publisher: Universitat de Barcelona
DOI: 10.5565/publmat6412001

Poisson summation formulas involving the sum-of-squares function

Author(s): Lev, Nir; Reti, Gilad
Published in: Israel Journal of Mathematics, Issue 246/1, 2021, Page(s) 403-421, ISSN 0021-2172
Publisher: Magnes Press
DOI: 10.1007/s11856-021-2252-8

A characterization of the weighted weak type Coifman–Fefferman and Fefferman–Stein inequalities

Author(s): Andrei K. Lerner
Published in: Mathematische Annalen, Issue 378/1-2, 2020, Page(s) 425-446, ISSN 0025-5831
Publisher: Springer Verlag
DOI: 10.1007/s00208-020-01980-z

Spectrality of Polytopes and Equidecomposability by Translations

Author(s): Nir Lev, Bochen Liu
Published in: International Mathematics Research Notices, 2019, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnz191

An example concerning Fourier analytic criteria for translational tiling

Author(s): Lev, Nir
Published in: Revista Matemática Iberoamericana, Issue 38/6, 2022, Page(s) 1975--1991, ISSN 0213-2230
Publisher: Universidad Autonoma de Madrid
DOI: 10.4171/rmi/1318

On the sharp upper bound related to the weakMuckenhoupt–Wheeden conjecture

Author(s): Andrei K. Lerner, Fedor Nazarov, Sheldy Ombrosi
Published in: Analysis & PDE, Issue 13/6, 2020, Page(s) 1939-1954, ISSN 2157-5045
Publisher: Mathematical Sciences Publishers
DOI: 10.2140/apde.2020.13.1939