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We characterize the measures on R which have both their support and spectrum uniformly discrete.
J.-P. Kahane, S. Mandelbrojt, Sur l’équation fonctionnelle de Riemann et la formule sommatoire de Poisson. Ann. Sci. École Norm. Sup. 75
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H. J. Landau, Necessary density conditions for sampling and interpolation of certain entire functions. Acta Math. 117
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Y. Meyer, Nombres de Pisot, nombres de Salem et analyse harmonique. Lecture Notes in Mathematics 117
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Y. Meyer, Algebraic numbers and harmonic analysis. North-Holland, Amsterdam, 1972
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E. Bombieri, J. E. Taylor, Quasicrystals, tilings, and algebraic number theory: some preliminary connections. The legacy of Sonya Kovalevskaya, Contemp. Math., vol. 64, Amer. Math. Soc., Providence, RI, 1987, pp. 241–264
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J. W. Cahn, J. E. Taylor, An introduction to quasicrystals. The legacy of Sonya Kovalevskaya, Contemp. Math., vol. 64, Amer. Math. Soc., Providence, RI, 1987, pp. 265–286
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A. Córdoba, La formule sommatoire de Poisson. C. R. Acad. Sci. Paris Sér. I Math. 306
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A. Córdoba, Dirac combs. Lett. Math. Phys. 17
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W. Rudin, Functional analysis. Second edition. McGraw-Hill, New York, 1991
1991
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Y. Meyer, Quasicrystals, diophantine approximation and algebraic numbers. Beyond quasicrystals (Les Houches, 1994), 3–16, Springer, Berlin, 1995
1995
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M. N. Kolountzakis, J. C. Lagarias, Structure of tilings of the line by a function. Duke Math. J. 82
1996
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J. C. Lagarias, Meyer’s concept of quasicrystal and quasiregular sets. Comm. Math. Phys. 179
1996
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R. V. Moody, Meyer sets and their duals. The mathematics of long-range aperiodic order (Waterloo, ON, 1995), 403–441, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 489, Kluwer Acad. Publ., Dordrecht, 1997
1997
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A. Olevskii, A. Ulanovskii, Universal sampling and interpolation of band-limited signals. Geom. Funct. Anal. 18
2008
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F. Dyson, Birds and frogs. Notices Amer. Math. Soc. 56
2009
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B. Matei, Y. Meyer, Simple quasicrystals are sets of stable sampling. Complex Var. Elliptic Equ. 55
2010
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M. Mitkovski, A. Poltoratski, Pólya sequences, Toeplitz kernels and gap theorems. Adv. Math. 224
2010
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S. Nitzan, A. Olevskii, Revisiting Landau’s density theorems for Paley-Wiener spaces. C. R. Math. Acad. Sci. Paris 350
2012
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A. Olevskii, A. Ulanovskii, On multi-dimensional sampling and interpolation. Anal. Math. Phys. 2
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V. P. Gurarii, Group methods of commutative harmonic analysis. Current problems in mathematics. Fundamental directions. Vol. 25 (Russian) Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1988. English translation in Commutative harmonic analysis II, edited by V. P. Havin and N. K. Nikolski. Springer-Verlag, Berlin, 1998
1998
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J. C. Lagarias, Mathematical quasicrystals and the problem of diffraction. Directions in mathematical quasicrystals, 61–93, CRM Monogr. Ser., 13, Amer. Math. Soc., Providence, 2000
2000
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M. Baake, D. Lenz, R. Moody, Characterization of model sets by dynamical systems. Ergod. Th. and Dynam. Sys. 27
2007
Cited alongside, same era.
2012
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N. Lev, A. Olevskii, Measures with uniformly discrete support and spectrum. C. R. Math. Acad. Sci. Paris 351
2013
Closest in time.
J.-P. Allouche, Y. Meyer, Quasicrystals, model sets, and automatic sequences. C. R. Physique 15
2014
Closest in time.