Non-linear sampling recovery based on quasi-interpolant wavelet representations. (English) Zbl 1175.41025
The author investigates a problem of approximate non-linear sampling recovery of functions on the unit interval of the real axis. Section 1 contains some known problems of sampling recovery of real univariate functions defined on the unit interval of the real axis. In Section 2 a quasi-interpolant wavelet representation of the B-splines for Besov spaces is obtained. Also some quasi-norm equivalences based on the above representation are proved. Section 3 contains some remarks regarding the linear and non-linear sampling recovery methods using quasi interpolant wavelet representations.
Reviewer: Dan Bārbosu (Baia Mare)
MSC:
| 41A46 | Approximation by arbitrary nonlinear expressions; widths and entropy |
Keywords:
non-linear sampling recovery; quasi-interpolant wavelet representation; adaptive choice; B-spline; Besov spaceReferences:
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