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P. L. Butzer, S. Ries and R. L. Stens, “Approximation of Continuous and Discontinuous Functions by Generalized Sampling Series,” Journal of Approximation Theory, Vol. 50, No. 1, 1987, pp. 25-39. doi:10.1016/0021-9045(87)90063-3

has been cited by the following article:

• 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 .