Abstract
This paper is concerned with Friedrichs extensions for a class of Hamiltonian systems. The non-symmetric problems are usually complicated and have unexpected properties. Here, Friedrichs extensions of a class of singular Hamiltonian systems including non-symmetric cases are characterized by imposing some constraints on each element of domains D ( H ) of the maximal operators H . These characterizations are given independent of principal solutions. It is interesting that by the results in the paper the Friedrichs extension of each of a large class of non-symmetric Hamiltonian systems has similar form to that of a symmetric Hamiltonian system. In addition, Friedrichs extensions of regular Hamiltonian systems are characterized incidently, J -self-adjoint Friedrichs extensions are studied, and a result is given for elements of D ( H ) , which makes the expression of the Friedrichs extension domain simpler. All results for Hamiltonian systems are finally applied to Sturm-Liouville operators with matrix-valued coefficients.
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