The exponential sampling formula has some limitations. By incorporating a Mellin bandlimited multiplier, we extend it to a wider class of functions with a series that converges faster. This series is a generalized exponential sampling series with some interesting properties. Moreover, under a side condition, any generalized exponential sampling series that is interpolating can be generated by a Mellin bandlimited multiplier. For an error analysis, we consider a truncated series with 2N+1 terms and look for a highest speed of convergence as tends to infinity. The results are illustrated by three examples.

Exponential sampling with a multiplier

Carlo Bardaro;Ilaria Mantellini;
2023

Abstract

The exponential sampling formula has some limitations. By incorporating a Mellin bandlimited multiplier, we extend it to a wider class of functions with a series that converges faster. This series is a generalized exponential sampling series with some interesting properties. Moreover, under a side condition, any generalized exponential sampling series that is interpolating can be generated by a Mellin bandlimited multiplier. For an error analysis, we consider a truncated series with 2N+1 terms and look for a highest speed of convergence as tends to infinity. The results are illustrated by three examples.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1549114
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