XXXVI Workshop on Geometric Methods in Physics 2-8.07.2017 VI School on Geometry and Physics 26-30.06.2017
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# Jiří Hrivnák

## Discrete Cosine and Sine transforms on Honeycomb lattice

The discrete Fourier-like analysis of generalized cosine and sine functions on the two-dimensional honeycomb lattice is presented. The theoretical background stems from the concept of Weyl-orbit functions, discretized simultaneously on the weight and root lattices of the Weyl group $A_2$. The introduced class of extended Weyl-orbit functions generalizes periodicity and boundary properties of the one-dimensional cosine and sine functions. Three types of discrete complex Fourier-Weyl transforms and three types of real-valued Hartley-Weyl transforms are detailed. Examples of unitary transform matrices and interpolation behavior of the discrete transform is demonstrated. Consequences of the developed discrete transforms for transversal eigenvibrations of the mechanical graphene model are discussed. This is a joint work with Lenka Motlochová.

 Event sponsored by: University of Bialystok

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