Quasicrystals and almost periodic functions
Annales Polonici Mathematici (1999)
- Volume: 72, Issue: 3, page 251-259
- ISSN: 0066-2216
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topZając, Mariusz. "Quasicrystals and almost periodic functions." Annales Polonici Mathematici 72.3 (1999): 251-259. <http://eudml.org/doc/262549>.
@article{Zając1999,
abstract = {We consider analogies between the "cut-and-project" method of constructing quasicrystals and the theory of almost periodic functions. In particular an analytic method of constructing almost periodic functions by means of convolution is presented. A geometric approach to critical points of such functions is also shown and illustrated with examples.},
author = {Zając, Mariusz},
journal = {Annales Polonici Mathematici},
keywords = {tilings; almost periodic functions; quasicrystals; Penrose tilings; Penrose quasiperiodic functions},
language = {eng},
number = {3},
pages = {251-259},
title = {Quasicrystals and almost periodic functions},
url = {http://eudml.org/doc/262549},
volume = {72},
year = {1999},
}
TY - JOUR
AU - Zając, Mariusz
TI - Quasicrystals and almost periodic functions
JO - Annales Polonici Mathematici
PY - 1999
VL - 72
IS - 3
SP - 251
EP - 259
AB - We consider analogies between the "cut-and-project" method of constructing quasicrystals and the theory of almost periodic functions. In particular an analytic method of constructing almost periodic functions by means of convolution is presented. A geometric approach to critical points of such functions is also shown and illustrated with examples.
LA - eng
KW - tilings; almost periodic functions; quasicrystals; Penrose tilings; Penrose quasiperiodic functions
UR - http://eudml.org/doc/262549
ER -
References
top- [1] V. I. Arnold, Remarks on quasicrystallic symmetries, Phys. D 33 (1988), 21-25. Zbl0684.52008
- [2] S. Bochner, Abstrakte fastperiodische Funktionen, Acta Math. 61 (1933), 149-184. Zbl59.0997.01
- [3] H. Bohr, Zur Theorie der fastperiodischen Funktionen, ibid. 45 (1925), 29-127.
- [4] N. G. de Bruijn, Algebraic theory of Penrose non-periodic tilings, Nederl. Akad. Wetensch. Proc. A84 (1981), 39-66. Zbl0457.05021
- [5] S. M. Guseĭn-Zade, The number of critical points of a quasiperiodic potential, Funct. Anal. Appl. 23 (1989), no. 2, 129-130. Zbl0711.58007
- [6] R. Penrose, Pentaplexity, Eureka 39 (1978), 16-22.
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