RETRACTED CHAPTER: Polynomial Frames

Polynomial frames are an emerging topic in the frame theory. Although traditional orthogonal polynomials can well approximate any data living in a region or the whole space, they lack the ability of localized spatial-frequency analysis and enough redundancy for robustness. Polynomial frames are generated by the combination of orthogonal polynomials and different windows. The data decomposition by polynomial frames can not only reveal localized spatial-frequency structure and evolution of data, but also conserve powerful computation ability and robustness. In this chapter, we mainly focus on Legendre-Trigonometric frames, Hermite frames, Laguerre frames and Chebyshev frames.