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Equal-norm tight frames with erasures. (English) Zbl 1035.42029

Given a Hilbert space H, a collection {e i :iI}H is called a frame if there exist constants A,B>0 such that for all fH:

Af 2 iI |f,e i | 2 Bf 2 ·

When A=B we say that the frame is tight. When all elements e i have the same norm, we say the frame is equal-norm, and when this norm is 1 we say the frame is normalized. The paper under review studies equal-norm tight frames in spaces R d and C d , equipped with the usual Euclidean inner product. Typical examples of such frames are harmonic frames, which consist of coordinates of the discrete Fourier transform. The authors show that all equal-norm tight frames generated by one or two unitary operators on R d (resp., C d ) are generalized harmonic frames. The last section of the paper is devoted to the study of frames that remain frames after deletion (erasure) of a finite number of its elements. Such frames are called robust to erasures, and harmonic frames have this property. Characterization of frames robust to k erasures is given.

MSC:
42C40Wavelets and other special systems
42C15General harmonic expansions, frames