*(English)*Zbl 1035.42029

Given a Hilbert space $H$, a collection $\{{e}_{i}:i\in I\}\subset H$ is called a frame if there exist constants $A,B>0$ such that for all $f\in H$:

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.