Multi-tiling and Riesz bases

被引：43

作者：

Grepstad, Sigrid ^{[1
]}

Lev, Nir ^{[2
,3
]}

机构：

[1] Norwegian Univ Sci & Technol NTNU, Dept Math Sci, NO-7491 Trondheim, Norway

[2] Ctr Recerca Matemat, Bellaterra 08193, Barcelona, Spain

[3] Bar Ilan Univ, Dept Math, IL-52900 Ramat Gan, Israel

来源：

ADVANCES IN MATHEMATICS | 2014年 / 252卷

基金：

以色列科学基金会;

关键词：

Riesz bases; Tiling; Quasicrystals; INTERPOLATING-SEQUENCES; QUASI-CRYSTALS; CONJECTURE; SETS;

D O I：

10.1016/j.aim.2013.10.019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let S be a bounded, Riemann measurable set in R-d, and Lambda be a lattice. By a theorem of Fuglede, if S tiles R-d with translation set Lambda, then S has an orthogonal basis of exponentials. We show that, under the more general condition that S multi-tiles R-d with translation set Lambda, S has a Riesz basis of exponentials. The proof is based on Meyer's quasicrystals. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：1 / 6

页数：6

共 50 条

[21] ON THE STABILITY OF FRAMES AND RIESZ BASES
FAVIER, SJ
ZALIK, RA
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 1995, 2 (02) : 160 - 173
[22] New Characterizations of Riesz Bases
Department of Mathematics, KAIST, 373-1, Kusong-Dong, Yusong-Gu, Taejon, 305-701, Korea, Republic of
Appl Comput Harmonic Anal, 2 (222-229):
[23] Unions of exponential Riesz bases
Lee, Dae Gwan
AIMS MATHEMATICS, 2024, 9 (09): : 23890 - 23908
[24] Riesz bases and multiresolution analyses
Zalik, RA
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 1999, 7 (03) : 315 - 331
[25] Combining Riesz bases in Rd
Kozma, Gady
Nitzan, Shahaf
REVISTA MATEMATICA IBEROAMERICANA, 2016, 32 (04) : 1393 - 1406
[26] Gabor orthonormal bases, tiling and periodicity
Pinos, Alberto Debernardi
Lev, Nir
MATHEMATISCHE ANNALEN, 2022, 384 (3-4) : 1461 - 1467
[27] Gabor orthonormal bases, tiling and periodicity
Alberto Debernardi Pinos
Nir Lev
Mathematische Annalen, 2022, 384 : 1461 - 1467
[28] Pseudobosons, Riesz bases, and coherent states
Bagarello, F.
JOURNAL OF MATHEMATICAL PHYSICS, 2010, 51 (02)
[29] Riesz bases of exponentials for partitions of intervals
Pfander, Goetz E.
Revay, Shauna
Walnut, David
2019 13TH INTERNATIONAL CONFERENCE ON SAMPLING THEORY AND APPLICATIONS (SAMPTA), 2019,
[30] Frames and Riesz bases: a short survey
Favier, SJ
Zalik, RA
WAVELET THEORY AND HARMONIC ANALYSIS IN APPLIED SCIENCES, 1997, : 93 - 117

← 1 2 3 4 5 →