1997 | OriginalPaper | Buchkapitel
Frames and Riesz bases: a short survey
verfasst von : S. J. Favier, R. A. Zalik
Erschienen in: Wavelet Theory and Harmonic Analysis in Applied Sciences
Verlag: Birkhäuser Boston
Enthalten in: Professional Book Archive
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Orthogonal bases provide a classical method to represent an element of a Hilbert space in terms of simpler ones. A Riesz basis is the image of an orthogonal basis under an invertible continuous linear mapping. In practical applications, when using orthogonal bases one introduces small truncation errors. As we shall see in the sequel, perturbing a Riesz bases (in particular, an orthogonal basis) by a small amount, yields another Riesz basis. This is one of the reasons that motivate the study of such bases.