The Fundamentals of Spectral Tetris Frame Constructions

Abstract

Abstract. In a landmark paper [9], Casazza, Fickus, Mixon, Wang and Zhou introduced a fundamental method for constructing unit norm tight frames, which they called Spectral Tetris. This was a significant advancement for finite frame theory -especially constructions of finite frames. This paper then generated a vast amount of literature as Spectral Tetris was steadily developed, refined, and generalized until today we have a complete picture of what are the broad applications as well as the limitations of Spectral Tetris. In this paper, we will put this vast body of literature into a coherent theory.

A brief introduction to Hilbert space frame theory and its applications

“…Another significant advance for frame theory came when Spectral Tetris was introduced by Casazza/Fickus/Mixon/Wang/Zhou [27]. This is now a massive subject and we refer the reader to a comprehensive survey of Casazza/Woodland [39]. We will just give an illustrative example here.…”