IJPAM: Volume 61, No. 4 (2010)
THE POLAR REPRESENTATION THEOREM
Grupo de Física-Matemática
Universidade de Lisboa
Professor Gama Pinto Av. 2, Lisboa, 1649-003, PORTUGAL
Departamento de Matemática
Faculdade de Ciências
Universidade de Lisboa, PORTUGAL
e-mail: [email protected]
Abstract.The polar representation theorem for the -dimensional time-dependent linear Hamiltonian system with continuous coefficients, states that, given two isotropic solutions and , with the identity matrix as Wronskian, the formula holds, where and are continuous matrices, and is symmetric.
In this article we use the monotonicity properties of the matrix eigenvalues in order to obtain results on the Sturm-Liouville problem.
Received: May 10, 2010
AMS Subject Classification: 34B24, 34C10, 34A30
Key Words and Phrases: Sturm-Liouville theory, Hamiltonian systems, polar representation
Source: International Journal of Pure and Applied Mathematics