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Fuglede's conjecture for a union of two intervals
Author(s):
I.
Laba
Journal:
Proc. Amer. Math. Soc.
129
(2001),
2965-2972.
MSC (2000):
Primary 42A99
Posted:
March 15, 2001
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Abstract:
We prove that a union of two intervals in  is a spectral set if and only if it tiles  by translations.
References:
-
- 1.
- E. M. Coven, A. Meyerowitz: Tiling the integers with translates of one finite set, J. Algebra 212 (1999), 161-174. MR 99k:11032
- 2.
- B. Fuglede: Commuting self-adjoint partial differential operators and a group theoretic problem, J. Funct. Anal. 16 (1974), 101-121. MR 57:10500
- 3.
- A. Iosevich, N. H. Katz, S. Pedersen: Fourier bases and a distance problem of Erdös, Math. Res. Lett. 6 (1999), 251-255. MR 2000j:42013
- 4.
- A. Iosevich, N. H. Katz, T. Tao: Convex bodies with a point of curvature do not have Fourier bases, Amer. J. Math, to appear.
- 5.
- A. Iosevich, N. H. Katz, T. Tao: preprint in preparation.
- 6.
- A. Iosevich, S. Pedersen: Spectral and tiling properties of the unit cube, Internat. Math. Res. Notices 16 (1998), 819-828. MR 2000d:52015
- 7.
- P. Jorgensen: Spectral theory of finite volume domains in
 , Adv. Math. 44 (1982), 105-120. MR 84k:47024 - 8.
- P. Jorgensen, S. Pedersen: Spectral theory for Borel sets in
 of finite measure, J. Funct. Anal. 107 (1992), 72-104. MR 93k:47005 - 9.
- P. Jorgensen, S. Pedersen: Spectral pairs in Cartesian coordinates, J. Fourier Anal. Appl. 5 (1999), 285-302. CMP 99:15
- 10.
- M. Kolountzakis: Non-symmetric convex domains have no basis of exponentials, Illinois J. Math. 44 (2000), 542-550. CMP 2000:16
- 11.
- M. Kolountzakis: Packing, tiling, orthogonality, and completeness, Bull. London Math. Soc. 32 (2000), 589-599. CMP 2000:15
- 12.
- J. C. Lagarias, J. A. Reed, Y. Wang: Orthonormal bases of exponentials for the
 -cube, Duke Math. J. 103 (2000), 25-37. CMP 2000:12 - 13.
- J. C. Lagarias, S. Szabó: Universal spectra and Tijdeman's conjecture on factorization of cyclic groups, J. Fourier Anal. Appl., to appear.
- 14.
- J. C. Lagarias, Y. Wang: Tiling the line with translates of one tile, Invent. Math. 124 (1996), 341-365. MR 96i:05040
- 15.
- J. C. Lagarias, Y. Wang: Spectral sets and factorizations of finite abelian groups, J. Funct. Anal. 145 (1997), 73-98. MR 98b:47011b
- 16.
- D. J. Newman: Tesselation of integers, J. Number Theory 9 (1977), 107-111. MR 55:2731
- 17.
- S. Pedersen: Spectral theory of commuting self-adjoint partial differential operators, J. Funct. Anal. 73 (1987), 122-134. MR 89m:35163
- 18.
- S. Pedersen: Spectral sets whose spectrum is a lattice with a base, J. Funct. Anal. 141 (1996), 496-509. MR 98b:47011a
- 19.
- S. Pedersen, Y. Wang: Universal spectra, universal tiling sets and the spectral set conjecture, Scand. J. Math., to appear.
- 20.
- R. Tijdeman: Decomposition of the integers as a direct sum of two subsets, London Math. Soc. Lecture Note Ser., vol.215, Cambridge Univ. Press, 1995, pp. 261-276. MR 96j:11025
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Additional Information:
I.
Laba
Affiliation:
Department of Mathematics, Princeton University, Princeton, New Jersey 08544
Address at time of publication:
Department of Mathematics, University of British Columbia, Vancouver, Canada V6T 1Z2
Email:
ilaba@math.ubc.ca
DOI:
10.1090/S0002-9939-01-06035-X
PII:
S 0002-9939(01)06035-X
Received by editor(s):
February 16, 2000
Posted:
March 15, 2001
Communicated by:
Christopher D. Sogge
Copyright of article:
Copyright
2001,
American Mathematical Society
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