Journal of Samara State Technical University, Ser. Physical and Mathematical SciencesJournal of Samara State Technical University, Ser. Physical and Mathematical Sciences1991-86152310-7081Samara State Technical University21032On representation of Parseval framesRyabtsovIgor Sаспирант, каф. функционального анализа и теории функций; Самарский государственный университет; Samara State Universitytinnulion@mail.ruSamara State University1506201115219419918022020Copyright © 2011, Samara State Technical University2011This 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.Parseval framesframe equivalencyframe representationsequiangular framestight framesфреймы Парсеваляэквивалентность фреймовпредставление фреймовравноугольные фреймыжёсткие фреймы[Christensen O. An introduction to frames and Riesz bases. Applied and Numerical Harmonic Analysis. Boston, MA: Birkhäuser Boston, Inc., 2003. 440 pp.][Casazza P. G., Tremain J. C. A brief introduction to Hilbert-space frame theory and its applications: preprint posted on www.framerc.org.][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.][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.][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.]