On Fuglede's Conjecture and the Existence of Universal Spectra

• Autores: M. Matolcsi, B. Farkas
• Localización: Journal of fourier analysis and its applications, ISSN 1069-5869, Vol. 12, Nº 5, 2006, págs. 483-494
• Idioma: francés
• DOI: 10.1007/s00041-005-5069-7
• Texto completo no disponible (Saber más ...)
• Referencias bibliográficas
  • Coven, E. M. and Meyerowitz, A. (1999). Tiling the integers with translates of one finite set, J. Algebra212(1), 161–174.
  • Farkas, B. and Révész, Sz. Gy. (2006). Tiles with no spectra in dimension 4, Math. Scand. 98(1), 44–52.
  • Fuglede, B. (1974). Commuting self-adjoint partial differential operators and a group theoretic problem,J. Funct. Anal. 16, 101–121.
  • Iosevich, A., Katz, N., and Tao, T. (2003). The Fuglede spectral conjecture holds for convex planar domains,Math. Res. Lett. 10(5-6), 559–569.
  • Iosevich, A., Katz, N. H., and Tao, T. (2001). Convex bodies with a point of curvature do not have Fourier bases, Amer. J. Math. 123(1), 115–120.
  • Kolountzakis, M. N. (2000). Nonsymmetric convex domains have no basis of exponentials, Illinois J. Math.44(3), 542–550.
  • Kolountzakis, M. N. and Matolcsi, M. (2006). Tiles with no spectra, Forum Math. 18, 519–528.
  • Kolountzakis, M. N. and Matolcsi, M. (2006). Complex Hadamard matrices and the spectral set conjecture,Collect. Math. Vol. Extra, 281–291.
  • Konyagin, S. and Łaba, I. (2003). Spectra of certain types of polynomials and tiling of integers with translates of finite sets, J. Number...
  • Łaba, I. (2001). Fuglede’s conjecture for a union of two intervals, Proc. Amer. Math. Soc. 129(10), 2965– 2972 (electronic).
  • Łaba, I. (2002). The spectral set conjecture and multiplicative properties of roots of polynomials, J. London Math. Soc. (2) 65(3), 661–671.
  • Łaba, I. and Wang, Y. Some properties of spectral measures, Appl. Comput. Harmon. Anal. to appear.
  • Lagarias, J. C. and Szabó, S. (2001). Universal spectra and Tijdeman’s conjecture on factorization of cyclic groups, J. Fourier Anal. Appl....
  • Lagarias, J. C. and Wang, Y. (1997). Spectral sets and factorizations of finite abelian groups, J. Funct. Anal.145(1), 73–98.
  • Matolcsi, M. (2005). Fuglede’s conjecture fails in dimension 4, Proc. Amer. Math. Soc. 133(10), 3021–3026.
  • Pedersen, S. and Wang, Y. (2001) . Universal spectra, universal tiling sets and the spectral set conjecture,Math. Scand. 88(2), 246–256.
  • Szegedy, M. (1998). Algorithms to tile the infinite grid with finite clusters, in 39th Annual Symposium on Foundations of Computer Science,...
  • Tao, T. (2004). Fuglede’s conjecture is false in 5 and higher dimensions, Math. Res. Lett. 11(2-3), 251–258.