Exponential sampling with a multiplier

The exponential sampling formula has some limitations. By incorporating a Mellin band limited 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 N -> infinity. We show by using a certain non-bandlimited multiplier, which introduces in addition an aliasing error, that we can achieve a higher rate of convergence to the function, namely O(e(-alpha N))with alpha>0,than with the truncated series of an exact formula. The results are illustrated by three examples.