Mathematics

Norm equalization in rows of orthogonal matrix and uniform frames

M. A. Lapshina

Dept. of Theory of Functions and Functional Analysis, Samara State University, Samara, 443011, Russia

Abstract: 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.

UDC: 517.51+517.98

Received: 09.02.2009
Revised: 09.02.2009