Abstract:
A brief overview of applications of Schoenberg’s polynomial B-splines of odd degrees in mathematical statistics, computational mathematics, and statistical radio engineering is provided. Exact formulas for the found Schoenberg B-spline of 15th degree are presented. High-quality approximations of smooth functions with an infinite Fourier transform by functions with a finite Fourier transform are found.
Key words:Schoenberg's B-splines of odd degrees, admissible estimates of probability density, spectral density estimate, analog linear filters, approximation of functions, summation of series.
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