Some notes on polynomial splines on the real axis

A.A. Selivanov

doi:10.15421/242531

Some notes on polynomial splines on the real axis

A.A. Selivanov (Oles Honchar Dnipro National University)

Abstract

We prove a number of properties of polynomial splines from the $$$L_p$$$ space on the real line, such as inclusion in other $$$L_q$$$ spaces and behavior at infinity of splines and their derivatives. Separately, we find the general form of a set of functions orthogonal to the space of polynomial splines with arbitrary smoothness.

Keywords

polynomial splines; Nikol’skii duality theorem; orthogonal sets

MSC 2020

Pri 41A15, 41A35, 41A44

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References

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