Construction of linearly independent and orthogonal functions in Hilbert function spaces via Wronski determinants
Athanasios Christou Micheas
Published: 2025/8/6
Abstract
Based on the Wronski determinant, we propose the construction of linearly independent orthogonal functions in any Hilbert function space. The method requires only an initial function from the space of the functions under consideration, that satisfies minimal properties. Two applications are considered, including solutions to ordinary differential equations and the construction of basis functions. We also present a conjecture that connects the latter two concepts, which leads to what we call the Wronski basis.