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arXiv · 1006.5718

The Sturm-Liouville problem and the Polar Representation Theorem

Jorge Rezende
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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.

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Jorge Rezende. 2010-06-29. The Sturm-Liouville problem and the Polar Representation Theorem. https://arxiv.org/abs/1006.5718

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