Norm equalization in rows of orthogonal matrix and uniform frames
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 2 (2009), pp. 51-59 Cet article a éte moissonné depuis la source Math-Net.Ru

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The simplified versions of Casazza–Leon algorithms for the construction of the uniform Parseval–Steklov frame of arbitrary volume from a block-diagonal orthogonal matrix are described in the paper. There are examples of uniform Parseval–Steklov frames of volume 5 in $\mathbb{R}^2$ and of volume 7 in $\mathbb{R}^3$.
Keywords: admissible sequence, frame, Parseval–Steklov frame, uniform frame, frame operator.
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     author = {M. A. Lapshina},
     title = {Norm equalization in rows of orthogonal matrix and uniform frames},
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M. A. Lapshina. Norm equalization in rows of orthogonal matrix and uniform frames. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 2 (2009), pp. 51-59. http://geodesic.mathdoc.fr/item/VSGU_2009_2_a4/

[1] Christensen O., An Introduction to Frames and Riesz Bases, Birkhäuser, Boston, 2002 | MR

[2] Drabkova E. S., Novikov S. Ya., “Ob'em freima Parsevalya”, Vestnik Samarskogo gosudarstvennogo universiteta, 2007, no. 9/1(59), 91–106 | MR

[3] Casazza P. G., Leonhard N., The known equal norm Parseval frames as of 2005, Rezhim dostupa: http://www.math.missouri.edu/<nobr>$\sim$</nobr>pete/

[4] Kolmogorov A. N., “K obosnovaniyu metoda naimenshikh kvadratov”, Uspekhi matematicheskikh nauk, 1:1 (1946), 57–70 | MR | Zbl

[5] Linnik Yu. V., Metod naimenshikh kvadratov, Fizmatgiz, M., 1962, 352 pp. | Zbl

[6] Casazza P. G., Leon N., Frames with a given frame operator, Rezhim dostupa: http://www.math.missouri.edu/<nobr>$\sim$</nobr>pete/

[7] Casazza P. G., Leon N., Existence and construction of finite tight frames, Rezhim dostupa: http:www.math.missouri.edu/<nobr>$\sim$</nobr>pete/

[8] Casazza P. G., Custom Building Finite Frames, Rezhim dostupa: http:www.math.missouri.edu/<nobr>$\sim$</nobr>pete/ | MR

[9] Lapshina M. A., “Ravnomernye freimy v prostranstve $\mathbb{R}^N$”, Vestnik Samarskogo gosudarstvennogo universiteta, 2008, no. 6, 112–122

[10] Khorn R., Dzhonson Ch., Matrichnyi analiz, Mir, M., 1989, 655 pp. | MR