Sampling expansions for functions of compact Mellin spectrum. (Q2776298)

The classical sampling theorem asserts that any bandlimited function can be reconstructed from the series of its uniform samples provided the sampling rate is at least twice as large as the largest frequency in its spectrum. The reconstruction formula, called the Whittaker-Kotelnikov-Shannon formula, or cardinal series, plays a central role in sampling theory and its applications.NEWLINENEWLINEIn this paper the author presents the corresponding sampling theorem for the case when the Fourier transform is replaced by the Mellin transform. Hence the usual bandlimited functions are replaced by functins that have a compact Mellin spectrum. The author also gives an interpretation of this result using so-called stretch invariant continuous linear systems where the system transfer operator commutes with the family of positive dilation operators.NEWLINENEWLINEFor the entire collection see [Zbl 0978.00017].