# 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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