On alternating functions in subspaces of - Shekhtman, Boris; Skrzypek, Lesław (Sampling theory, signal processing, and data analysis, 2025)
In this short paper we improve on the result from (Singer, Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces, 1970) (Lemma 6.1) and based on that we show that any dimensional subspace of admits –alternating function , i.e., a non-zero function , for which there exists points such that