Spectral and Tiling Properties of the Unit Cube

International Mathematics Research Notices

Volumn , Issue 16, 1998, Pages

  Iosevich, Alex ^a   Pedersen, Steen ^b  

^a GEORGETOWN UNIVERSITY   (United States)

^b WRIGHT STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1842729485     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. K. Corrádi and S. Szabó, A combinatorial approach for Keller's conjecture, Period. Math. Hungar. 21 (1990), 95-100.
2. B. Fuglede, Commuting self-adjoint partial differential operators and a group theoretic problem, J. Funct. Anal. 16 (1974), 101-121.
3. D. Girault-Beauquier and M. Nivat, "Tiling the plane with one tile" in Topology and Category Theory in Computer Science (Oxford, 1989), G. M. Reed, A. W. Roscoe, and R. F. Wachter, eds., Oxford Univ. Press, New York, 1991, 291-333.
4. G. Hajós, Über einfache und mehrfache Bedeckung des n-dimensionalen Raumes mit einen Wärfeigitter, Math. Z. 47 (1942), 427-467.
5. n of finite measure, J. Funct. Anal. 107 (1992), 72-104.
6. _, Spectral pairs in Cartesian coordinates, preprint, 1997.
7. O. H. Keller, Über die lückenlose Einfüllung des Raumes mit Würfeln, J. Reine Angew Math. 163 (1930), 231-248.
8. J. C. Lagarias, J. A. Reed, and Y. Wang, Orthonormal bases of exponentials for the n-cube, preprint, 1998.
9. J. C. Lagarias and P. Shor, Keller's cube-tiling conjecture is false in high dimensions, Bull. Amer. Math. Soc. 27 (1992), 279-283.
10. J. C. Lagarias and Y. Wang, Tiling the line with translates of one tile, Invent. Math. 124 (1996), 341-365.
11. n, Adv. Math. 121 (1996), 21-49.
12. _, Spectral sets and factorizations of finite abelian groups, J. Funct. Anal. 145 (1997), 73-98.
13. S. Pedersen, Spectral theory of commuting selfadjoint partial differential operators, J. Funct. Anal. 73 (1987), 122-134.
14. _, Spectral sets whose spectrum is a lattice with a base, J. Funct. Anal. 141 (1996), 496-509.
15. O. Perron, Über lückenlose Ausfüllung des n-dimensionalen Raumes durch kongruente Würfel, I, Math. Z. 46 (1940), 1-26; II, 161-180.
16. O. Perron, Über lückenlose Ausfüllung des n-dimensionalen Raumes durch kongruente Würfel, I, Math. Z. 46 (1940), 1-26; II, 161-180.
17. M. Reed and B. Simon, Methods of modern mathematical physics, I: Funtional Analysis, Academic Press, New York, 1972.
18. S. Stein and S. Szabó, Algebra and Tiling: Homomorphisms in the Service of Geometry, Cams Math. Monogr. 25, Math. Assoc. America, Washington, D.C., 1994.
19. S. Szabó, A reduction of Keller's conjecture, Period. Math. Hungar. 17 (1986), 265-277.