Localization of the generalized sampling series and its numerical application. (English) Zbl 1105.94003
Summary: We study the localization of the sampling series with general kernel and obtain its error estimates. To achieve exponentially decaying accuracy for the series to approximate a band-limited function and its derivatives, a sufficient condition is given and a rigorous criterion is provided for the sampling to obtain any desired accuracy. The result includes several known results as special cases and gives new results about wavelet sampling series.
MSC:
| 94A20 | Sampling theory in information and communication theory |
| 41A30 | Approximation by other special function classes |
| 41A25 | Rate of convergence, degree of approximation |
| 65D25 | Numerical differentiation |
| 65D15 | Algorithms for approximation of functions |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
