Optimal recovery of mappings based on linear information with the help of $$$T$$$-splines in Banach spaces

Abstract

This work is dedicated to solving problems of optimal recovery of operator $$$A$$$ (not necessarily linear), defined on a subset $$$\mathfrak{M}$$$ of a Banach space $$$H$$$ using information  about elements of the $$$\mathfrak{M}$$$, given by a linear bounded operator $$$T\colon H\to Y$$$ where $$$Y$$$ is some Banach space. We show that under certain condition the optimal method of recovery is given by abstract interpolation splines in $$$H$$$ generated by $$$T$$$ ($$$T$$$-interpolating splines).