TY - GEN
T1 - Patterns in Fourier Space
AU - Scheurle, Jürgen
N1 - Publisher Copyright:
© Springer International Publishing AG 2017.
PY - 2017
Y1 - 2017
N2 - In this article we study how symmetries (invariance properties with respect to appropriate group actions) of periodic and quasiperiodic functions on Rn(n∈ N) manifest themselves as patterns in Fourier space, i.e. as specific relations between certain Fourier coefficients of such a function. This is motivated by the experimental method of X-ray diffraction in crystallography, by which the atomic structure within a crystal can be determined. Mathematically, this tool heavily relies on Fourier analysis. In fact, it (approximately) produces the Fourier expansion of the corresponding electron density distribution function. Our results confirm that especially certain symmetries of this function are detected in that way. The case of quasiperiodic functions is related to quasicrystals.
AB - In this article we study how symmetries (invariance properties with respect to appropriate group actions) of periodic and quasiperiodic functions on Rn(n∈ N) manifest themselves as patterns in Fourier space, i.e. as specific relations between certain Fourier coefficients of such a function. This is motivated by the experimental method of X-ray diffraction in crystallography, by which the atomic structure within a crystal can be determined. Mathematically, this tool heavily relies on Fourier analysis. In fact, it (approximately) produces the Fourier expansion of the corresponding electron density distribution function. Our results confirm that especially certain symmetries of this function are detected in that way. The case of quasiperiodic functions is related to quasicrystals.
KW - Application of group representations in physics
KW - Crystalline structure
KW - Fourier coefficients and fourier series
KW - Invariance and symmetry properties
KW - Pattern recognition
KW - Trigonometric series
UR - http://www.scopus.com/inward/record.url?scp=85044474481&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-64173-7_2
DO - 10.1007/978-3-319-64173-7_2
M3 - Conference contribution
AN - SCOPUS:85044474481
SN - 9783319641720
T3 - Springer Proceedings in Mathematics and Statistics
SP - 16
EP - 27
BT - Patterns of Dynamics - In Honour of Bernold Fiedler’s 60th Birthday
A2 - Gurevich, Pavel
A2 - Hell, Juliette
A2 - Scheel, Arnd
A2 - Sandstede, Bjorn
PB - Springer New York LLC
T2 - Conference on Patterns of Dynamics held in honor of Bernold Fiedler’s 60th Birthday, 2016
Y2 - 25 July 2016 through 29 July 2016
ER -