TITLE:
Computing Recomposition of Maps with a New Sampling Asymptotic Formula
AUTHORS:
Almudena Antuña, Juan L. G. Guirao, Miguel A. López
KEYWORDS:
Band-Limited Signal, Shannon's Sampling Theorem, Approximation Theory
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.1 No.2,
July
6,
2011
ABSTRACT: The aim of the present paper is to state an asymptotic property Ρ 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 Ρ is fulfilled for any constant signal working for every given sampling frequency. Moreover, we conjecture that Gaussian maps of the form e-Λt2 ,Λ∈R+, hold Ρ. We support this conjecture by proving the equality given by for the three first coefficients of the power series representation of e-Λt2 .