Discontinuous Linear Hamiltonian Systems

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FILOMAT, vol.36, no.3, pp.813-827, 2022 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.2298/fil2203813a
  • Title of Journal : FILOMAT
  • Page Numbers: pp.813-827
  • Keywords: Hamiltonian system, transmission conditions, maximal operator, minimal operator, self-adjoint operator, spectral resolution, BOUNDARY-VALUE-PROBLEMS, PERIODIC-SOLUTIONS, M(LAMBDA) THEORY, CONTROLLABILITY, PENDULUM


We study a discontinuous linear Hamiltonian system. We obtain a result on the existence and uniqueness of solutions. Later, we introduce the corresponding maximal and minimal operators for this problem and the self-adjoint extensions of such a minimal operator are established. Finally, we obtain an eigenfunction expansion.