Uğurlu, EkinUğurlu, Ekin2023-02-142023-02-142020Uğurlu, Ekin (2020). "A new Hamiltonian system", Journal of Mathematical Analysis and Applications, Journal of Mathematical Analysis and Applications, Vol. 491, No. 2.0022-247Xhttps://hdl.handle.net/20.500.12416/6224This paper aims to share a new first-order differential equation that contains the continuous analogous of the orthogonal polynomials on the unit-circle. We introduce some basic results on the system and solutions of the system. Using nested-circle approach we introduce the possible number of square-integrable solutions of the system. At the end of the paper we share a limit-point criteria for the two-dimensional system of equations.eninfo:eu-repo/semantics/closedAccessFirst-Order SystemOrthogonal Polynomials on The Unit CircleWeyl's TheoryArticle491210.1016/j.jmaa.2020.124392