The Sturm-Liouville problem and the Polar Representation Theorem
Classical Analysis and ODEs
2010-07-01 v1 Mathematical Physics
math.MP
Abstract
The polar representation theorem for the n-dimensional time-dependent linear Hamiltonian system with continuous coefficients, states that, given two isotropic solutions (Q1, P1) and (Q2, P2), with the identity matrix as Wronskian,the formula Q2 = rcos(f), Q1 = rsin(f), holds, where r and f are continuous matrices, r is non-singular and f is symmetric. In this article we use the monotonicity properties of the matrix f eigenvalues in order to obtain results on the Sturm-Liouville problem.
Keywords
Cite
@article{arxiv.1006.5718,
title = {The Sturm-Liouville problem and the Polar Representation Theorem},
author = {Jorge Rezende},
journal= {arXiv preprint arXiv:1006.5718},
year = {2010}
}