Non oscillatory functions and a fourier inversion theorem for functions of very moderate decrease

Author(s): Tristram de Piro1
1Flat 3, Redesdale House, 85 The Park, Cheltenham, GL50 2RP.
Copyright © Tristram de Piro. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider non oscillatory functions and prove an everywhere Fourier Inversion Theorem for functions of very moderate decrease. The proofs rely on some ideas in nonstandard analysis.

Keywords: Kernels, Lagrangian Multiplier, least square, Olanrewaju-Olanrewaju regression-type, nonparametric regression, support vector regressor (SVR)