SciELO - Scientific Electronic Library Online

vol.20 issue2New method for the analysis of images: the square wave methodSea level rise and the geoid: factor analysis approach author indexsubject indexarticles search
Home Pagealphabetic serial listing  

Services on Demand




Related links

  • Have no similar articlesSimilars in SciELO


Revista de Matemática Teoría y Aplicaciones

Print version ISSN 1409-2433

Rev. Mat vol.20 n.2 San José Jul./Dec. 2013


Symmetry orbits and their data-analytic properties

Órbitas de simetría y sus propiedades en análisis de datos

Marlos A.G. Viana*+

*Dirección para correspondencia:


The concept of data indexed by finite symmetry orbits is reviewed within the data-analytic framework of symmetry studies. Data decompositions are discussed in terms of canonical projections and Plancherel’s formulas, and interpreted in terms of orbit invariants.

Keywords: irreducible representations, irreducible characters, finite groups, canonical projections, Fourier transforms, convolution.


Se revisa el concepto de datos indexados por órbitas simétricas finitas en el marco de estudios de simetría. Se discute la descomposición de datos en términos de proyecciones canónicas y fórmulas de Plancherel, e interpretada en términos de órbitas invariantes.

Palabras clave: representaciones irreducibles, características irrducibles, grupos finitos, proyecciones canónicas, transformada de Fourier, convolución.

Mathematics Subject Classification: 60B15, 60F05, 05E05.

Contenido disponible en pdf


[1] Viana, M.; Lakshminarayanan, V. (2013) Dihedral Fourier Analysis: Data-Analytic Aspects and Applications. Lecture Notes in Statistics 206, Springer, New York, N.Y.         [ Links ]

[2] Viana, M. (2008) Symmetric Studies: An Introduction to the Analysis of Structured Data in Applications. Cambridge University Press, New York, N.Y.         [ Links ]

[3] Weyl, H. (1977) The Classical Groups: Their Invariants and Representations. Princeton University Press, Landmarks in Mathematics and Physics. Original work (1939).         [ Links ]

*Correspondencia a:
Marlos A.G. Viana. University of Illinois at Chicago Eye Center, Chicago, Illinois, U.S.A. E-Mail:
*University of Illinois at Chicago Eye Center, Chicago, Illinois, U.S.A. E-Mail:

Received: 31/Jan/2013; Revised: 17/May/2013; Accepted: 28/May/2013

Creative Commons License All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License