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Strungaru, Nicolae. Positive Definite Measures with Discrete Fourier Transform and Pure Point Diffraction. Canadian mathematical bulletin, Tome 54 (2011) no. 3, pp. 544-555. doi: 10.4153/CMB-2011-059-x
@article{10_4153_CMB_2011_059_x,
author = {Strungaru, Nicolae},
title = {Positive {Definite} {Measures} with {Discrete} {Fourier} {Transform} and {Pure} {Point} {Diffraction}},
journal = {Canadian mathematical bulletin},
pages = {544--555},
year = {2011},
volume = {54},
number = {3},
doi = {10.4153/CMB-2011-059-x},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-059-x/}
}
TY - JOUR AU - Strungaru, Nicolae TI - Positive Definite Measures with Discrete Fourier Transform and Pure Point Diffraction JO - Canadian mathematical bulletin PY - 2011 SP - 544 EP - 555 VL - 54 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-059-x/ DO - 10.4153/CMB-2011-059-x ID - 10_4153_CMB_2011_059_x ER -
%0 Journal Article %A Strungaru, Nicolae %T Positive Definite Measures with Discrete Fourier Transform and Pure Point Diffraction %J Canadian mathematical bulletin %D 2011 %P 544-555 %V 54 %N 3 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-059-x/ %R 10.4153/CMB-2011-059-x %F 10_4153_CMB_2011_059_x
[1] [1] Argabright, L. and de Lamadrid, J. Gil, Fourier analysis of unbounded measures on locally compact abelian groups. Memoirs of the American Mathematical Society, 145, American Mathematical Society, Providence, RI, 1974. Google Scholar
[2] [2] Baake, M. and Lenz, D., Dynamical systems on translation bounded measures: pure point dynamical and diffraction spectra. Ergodic Theory Dynam. Systems 24(2004), no. 6, 1867–1893. doi:10.1017/S0143385704000318 Google Scholar
[3] [3] Baake, M. and Moody, R. V.,Weighted Dirac combs with pure point diffraction. J. Reine Angew. Math. 573(2004), 61–94. Google Scholar
[4] [4] Berg, C. and Forst, G., Potential theory on locally compact abelian groups. Ergebnisse der Mathematik und ihrer Grenzgebiete, 87, Springer-Verlag, New York-Heidelberg, 1975. Google Scholar
[5] [5] Dworkin, S., Spectral theory and X-ray diffraction. J. Math. Phys. 34(1993), no. 7, 2965–2967. doi:10.1063/1.530108 Google Scholar
[6] [6] Eberlein, W. F., A Note on Fourier-Stieltjes transforms. Proc. Amer. Math. Soc. 6(1955), 310–312. doi:10.1090/S0002-9939-1955-0068030-2 Google Scholar
[7] [7] Gouéré, J. B., Quasicrystals and almost periodicity. Comm. Math. Phys. 225(2005), no. 3, 655–681. doi:10.1007/s00220-004-1271-8 Google Scholar
[8] [8] Hewitt, E. and Ross, K. A., Abstract harmonic analysis. II. Structure and analysis for compact groups. Analysis on locally compact Abelian groups. Die Grundlehren der mathematischenWissenschaften, 152, Springer-Verlag, New York-Berlin 1970. Google Scholar
[9] [9] Hof, A., Diffraction by aperiodic structures. Commun. Math. Phys. 169(1995), no. 1, 25–43. doi:10.1007/BF02101595 Google Scholar
[10] [10] Gil. de Lamadrid, J. and Argabright, L. N, Almost periodic measures. Mem. Amer. Math. Soc. 28(1990), no. 428. Google Scholar
[11] J-Y., Lee, Moody, R. V., and Solomyak, B., Pure point dynamical and diffraction spectra. Ann. Henri Poincaré 3(2002), no. 5, 1003–1018. doi:10.1007/s00023-002-8646-1 Google Scholar
[12] [12] Lenz, D. and Strungaru, N., Pure point spectrum for measurable dynamical systems on locally compact abelian groups. J. Math. Pures Appl. 92(2009), no. 4, 323–341. Google Scholar
[13] [13] Moody, R. V. and Strungaru, N., Point sets and dynamical systems in the autocorrelation topology. Canad. Math. Bull. 47(2004), no. 1, 82–99. doi:10.4153/CMB-2004-010-8 Google Scholar
[14] [14] Schlottmann, M., Cut-and-project sets in locally compact abelian groups. In: Quasicrystals and discrete geometry (Toronto, ON, 1995), Fields Inst. Monogr., 10, American Mathematical Society, Providence, RI, 1998, pp. 247–264. Google Scholar
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