Computing recomposition of maps with a new sampling asymptotic formula
2011 - A. Antuna, J.L. Guirao, M.A. López
Open Journal of Discrete Mathematics. 1, 43-49 (2011)
The aim of the present paper is to state an asymptotic property ? of Shannon’s sampling theorem type, based on normalized cardinal sines, and keeping constant the sampling frequency of a not necessarilly band- limited signal. It generalizes in the limit the results stated by Marvasti et al. [7] and Agud et al. [1]. We show that ? is fulfilled for any constant signal working for every given sampling frequency. Moreover, we conjecture that Gaussian maps of the form e-?t2 ,??R+, hold ?. We support this conjecture by proving the equality given by for the three first coefficients of the power series representation of e-?t2 .