Decomposition matrices for the special case of data on the triangular lattice of SU(3)

  title={Decomposition matrices for the special case of data on the triangular lattice of SU(3)},
  author={M. Bodner and J. Patera and M. Szajewska},
  journal={Applied and Computational Harmonic Analysis},
Abstract A method for the decomposition of data functions sampled on a finite fragment of triangular lattice is described for the cases of lattices of any density corresponding to the simple Lie group G ( 2 ) . Its main advantage is the fact that the decomposition matrix needs to be calculated only once for arbitrary sets of data sampled on the same set of discrete points. The decomposition matrix applies to lattice of any density that carries data. 
Decomposition matrices for the square lattices of the Lie groups $$SU(2)\times SU(2)$$SU(2)×SU(2)
A method for the decomposition of data functions sampled on a finite fragment of rectangular lattice is described. The symmetry of a square lattice in a 2-dimensional real Euclidean space is eitherExpand
Central Splitting of A2 Discrete Fourier-Weyl Transforms
The central splitting of any function carrying the data into a sum of components governed by the number of elements of the center of A2 is employed to reduce the original weight lattice Fourier–Weyl transform into the corresponding weight lattices splitting transforms. Expand
Construction of graphene, nanotubes and polytopes using finite reflection groups
A reduction of orbits of finite reflection groups to their reflection subgroups is produced by means of projection matrices, which transform points of the orbit of any group to points of the orbitsExpand
The Discrete Cosine Transform on Triangles
  • B. Seifert, K. Hüper
  • Mathematics, Computer Science
  • ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
  • 2019
This paper has shown how one can define an analogue of the discrete cosine transform on triangles by combining algebraic signal processing theory with a specific kind of multivariate Chebyshev polynomials. Expand


Computation of character decompositions of class functions on compact semisimple Lie groups
A new algorithm is described for splitting class functions of an arbitrary semisimple compact Lie group K into sums of irreducible characters. The method is based on the use of elements of finiteExpand
Three-dimensional C-, S- and E-transforms
Three-dimensional continuous and discrete Fourier-like transforms, based on the three simple and four semisimple compact Lie groups of rank 3, are presented. For each simple Lie group, there areExpand
On Discretization of Tori of Compact Simple Lie Groups
Three types of numerical data are provided for simple Lie groups of any type and rank. This data is indispensable for Fourier-like expansions of multidimensional digital data into finite series ofExpand
Four types of special functions of G 2 and their discretization
Properties of four infinite families of special functions of two real variables, based on the compact simple Lie group G 2, are compared and described. Two of the four families (called here C- andExpand
E-Orbit Functions
We review and further develop the theory of E-orbit functions. They are func- tions on the Euclidean spaceEn obtained from the multivariate exponential function by sym- metrization by means of anExpand
Chebyshev polynomials : from approximation theory to algebra and number theory
Definitions and Some Elementary Properties Extremal Properties Expansion of Functions in Series of Chebyshev Polynomials Iterative Properties and Some Remarks About the Graphs of the Tn SomeExpand
The processing of hexagonally sampled two-dimensional signals
Methods for the processing of two- dimensional signals which have been sampled as two-dimensional hexagonal arrays are presented and some comparisons between the two methods for representing planar data will also be presented. Expand
Digital Signal Processing: A Computer-Based Approach
A number of new topics have been added to the second edition of "Digital Signal Processing: A Computer-Based Approach", based on user feedback, and the author has taken great care to organize the chapters more logically by reordering the sections within chapters. Expand
Hexagonal Image Processing: A Practical Approach
This paper presents a comparison of the practical aspects of hexagonal image processing on square and hexagonal grids and discusses the proposed HIP framework. Expand
Introductory Digital Image Processing: A Remote Sensing Perspective
Introductory Digital Image Processing: A Remote Sensing Perspective focuses on digital image processing of aircraft- and satellite-derived, remotely sensed data for Earth resource management applications. Expand