On representation of Parseval frames


This paper investigates properties of Parseval frames in finite dimensional vector spaces, namely, the possibility of representing some frames as sums of others. A new approach in constructing arbitrary Parseval frames and the decomposition arbitrary frame into the sum are described. Besides there is a number of special properties of equiangular tight frames.

About the authors

Igor S Ryabtsov

Samara State University

Email: tinnulion@mail.ru
аспирант, каф. функционального анализа и теории функций; Самарский государственный университет; Samara State University


  1. Christensen O. An introduction to frames and Riesz bases. Applied and Numerical Harmonic Analysis. Boston, MA: Birkhäuser Boston, Inc., 2003. 440 pp.
  2. Casazza P. G., Tremain J. C. A brief introduction to Hilbert-space frame theory and its applications: preprint posted on www.framerc.org.
  3. Истомина М. Н., Певный А. Б. О расположении точек на сфере и фрейме Мерседес- Бенц / Матем. просв., сер. 3, Т. 11. М.: Изд-во МЦНМО, 2007. С. 105-112.
  4. Novikov S. Ya., Ryabtsov I. S. Optimization of Frame Representations for Compressed Sensing and Mercedes-Benz Frame // Proc. Steklov Inst. Math., 2009. Vol. 265. Pp. 199-207.
  5. Casazza P. G., Redmond D., Tremain J. C. Real equiangular frames / In: Proc. 42th Annu. Conf. Information Sciences and Systems (CISS 2008). Princeton, NJ, 2008. Pp. 715-720.



Abstract - 38

PDF (Russian) - 24


Article Metrics

Metrics Loading ...


  • There are currently no refbacks.

Copyright (c) 2011 Samara State Technical University

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies