The Wronski orthogonalization process in Hilbert function spaces

Abstract

Based on the Wronski determinant, we propose the construction of linearly independent and orthogonal functions in any Hilbert function space. We call the new method the Wronski orthogonalization process. The method requires only an initial function from the space of functions under consideration, that satisfies mild conditions, and emerges as a generalization of the Gram-Schmidt process. Two applications are considered, including solutions to ordinary differential equations and the construction of basis functions in Hilbert function spaces. We also present a conjecture that connects the latter two concepts, which leads to the introduction of the Wronski basis.

Title Change, 20 pages; generalization of Gram-Schmidt orthonormalization; construction of basis functions; differential equations and Wronski basis; conjecture on bases in Hilbert spaces