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

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

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