Universal spectra, universal tiling sets and the spectral set conjecture

By S. Pedersen, Yang Wang. 2001

65 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/f52b7d884e8cbd0d7b44eb6241d644208158546e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Mathematical Physics

In Numerical Analysis

Citations in the corpus

ON THE SPECTRA OF A CANTOR MEASURE (2008, background): “We refer to [11,13,16,17] for some important results and developments related to the spectral pairs with respect to probability measures that are obtained by restricting the Lebesgue measure to bounded sets.”
Some reductions of the spectral set conjecture to integers (2013, background): “Results of this type are scattered in the literature [2, 3, 8, 10, 12, 13, 15].”
Tiles with no spectra (2004, background): “The Spectral Set Conjecture has attracted considerable attention in the last decade, revealing a wealth of connections to functional analysis, combinatorics, commutative algebra, number theory and Fourier analysis (the papers [1, 2, 3, 4, 5, 6, 7, 8, 10, 12] and references therein give a more or les”
FOURIER SERIES ON FRACTALS: A PARALLEL WITH WAVELET THEORY (2007, background): “Very importantly, in his 1974 paper, Fuglede calculated a number of instructive examples that showed the significance of combinatorics and of finite cyclic groups in our understanding of spectrum and tilings; and he made precise what is now referred to as the Fuglede conjecture ([JP94, JP00, PW01 ,”
Spectrality of Self-Similar Tiles (2013, background): “2 in [40], starting with Zb = {0} ⊕ Zb), we have Zb = C0 ⊕ C1 ⊕ · · · ⊕ Cm .”
Analysis of orthogonality and of orbits in affine iterated function systems (2006, methodology): “Since then they have been used extensively in harmonic analysis, in varied contexts involving the analysis of Fourier bases and geometry in for example the papers [Haa96, IoPe98, IoKaPe99, PeWa01 , LaWa96, LaWa97, Tao04] among others.”
The spectral set conjecture and multiplicative properties of roots of polynomials (2000, unknown): “C”
Some properties of spectral measures (2006, unknown): “Lagarias and Wang [LaWa97b], Pedersen and Wang [ PeWa01 ], Laba [Lab01], and Iosevich, Katz and Tao [IKT03].”
The Spectral Set Conjecture and Multiplicative Properties of Roots of Polynomials (2002, methodology): “(Note that such polynomials were also used in [ 23 ].) Clearly, A ⊂ Z tiles Z if and only if A+[0, 1) tiles R, hence the relevance of this work to the problem under consideration.”