The finite section method and problems in frame theory. (English) Zbl 1078.42024
The finite section method applies for approximation of frame operators and their inverses. The paper under review presents a computable refinement of the finite section method in the two above mentioned cases. This is achieved by restricting the attention to finite matrices. Special attention is given to frames which are polynomially or exponentially localized with respect to some orthonormal basis. The rates of approximation for these cases are given. Several applications are provided.
Reviewer: Wojciech Czaja (Wien)
MSC:
| 42C15 | General harmonic expansions, frames |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
Keywords:
frames; finite section method; inverse frame operator; shift-invariant system; localized frameReferences:
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