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3 September 2009 When are frames close to equal-norm Parseval frames?
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We derive lower and upper bounds for the distance between a frame and the set of equal-norm Parseval frames. The lower bound results from variational inequalities. The upper bound is obtained with a technique that uses a family of ordinary differential equations for Parseval frames which can be shown to converge to an equal-norm Parseval frame, if the number of vectors in a frame and the dimension of the Hilbert space they span are relatively prime, and if the initial frame consists of vectors having sufficiently nearly equal norms.
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Bernhard G. Bodmann and Peter G. Casazza "When are frames close to equal-norm Parseval frames?", Proc. SPIE 7446, Wavelets XIII, 744616 (3 September 2009);

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