Orthonormal bases of exponentials for the n-cube

Duke Mathematical Journal

Volumn 103, Issue 1, 2000, Pages 25-37

  Lagarias, Jeffrey C ^a   Reeds, James A ^a   Wang, Yang ^b  

^a AT AND T LABS RESEARCH   (United States)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002355528     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-00-10312-2     Document Type: Article

References (17)

1. B. Fuglede, Commuting self-adjointpartial differential operators and a group theoreticprob-lem, J. Funct. Anal. 16 (1974), 101-121.
2. K. Grochenig and H. Razafinjatovo, On Landau's necessary density conditions for sam-plingandinterpolation of band-limited functions, J. London. Math. Soc. (2) 54 (1996), 557-565.
3. A. Iosevich and S. Pedersen, Spectral and tilingproperties of the unit cube, Internat. Math. Res. Notices 1998, 819-828.
4. n offinite measure, J. Funct. Anal. 107 (1992), 72-104.
5. P. E. T. Jorgensen and S. Pedersen, Group-theoretic and geometric properties of multivariable Fourier series, Exposition. Math. 11 (1993), 309-329.
6. P. E. T. Jorgensen and S. Pedersen, Spectralpairs in Cartesian coordinates, J. Fourier Anal. Appl. 5 (1999), 285-302.
7. O. H. Keller, Über die lückenlose Einfüllung des Raumes mit Würfeln, J. Reine Angew. Math. 163 (1930), 231-248.
8. M. Kolountzakis, Packing, tiling, orthogonality and completeness, preprint, http://xxx.lanl.gov/abs/math.CA/9904066.
9. J. C. Lagarias and P. Shor, Keller's cube-tiling conjecture is false in high dimensions, Bull. Amer. Math. Soc. (N.S.) 27 (1992), 279-283.
10. J. C. Lagarias and Y. Wang, Spectral sets and factorizations offinite abelian groups, J. Funct. Anal. 145 (1997), 73-98.
11. H. Landau, Necessary density conditions for sampling and interpolation of certain entire functions, Acta Math. 117 (1967), 37-52.
12. H. Landau, Sampling, data transmission and the Nyquist rate, Proc. IEEE 55 (1967), 1701-1706.
13. S. Pedersen, Spectral theory of commuting selfadjointpartial differential operators, J. Funct. Anal. 73 (1987), 122-134.
14. S. Pedersen, Spectral sets whose spectrum is a lattice with a base, J. Funct. Anal. 141 (1996), 496-509.
15. O. Perron, Überlückenlose Ausfüllung des n-dimensionalen Raumes durch kongruente Würfel, Math. Z. 46 (1940), 1-26
16. O. Perron, Überlückenlose Ausfüllung des n-dimensionalen Raumes durch kongruente Würfel II, Math. Z. 46 (1940), 161-180.
17. E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Math. Ser. 32, Princeton Univ. Press, Princeton, 1971.