Abstract
Spectral Tetris is a powerful tool for constructing sparse equal norm Hilbert space frames. We introduce a new form of Spectral Tetris which works for non-equal-norm frames. It is known that this method cannot construct all frames—even in the new case introduced here. Until now, it has been a mystery why Spectral Tetris sometimes works and sometimes fails. We provide a complete answer by giving necessary and sufficient conditions for Spectral Tetris to construct frames with prescribed vector norms and prescribed frame operator. We present a variety of examples and include cases where Spectral Tetris always works.
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