On the Maximal Subspaces of Discrete Hamiltonian Systems
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Abstract
In this paper, we consider a discrete Hamiltonian system on nonnegative integers, and using Sylvester's inertia indices theory, we construct maximal subspaces on which the Hermitian form has a certain sign. After constructing nested ellipsoids, we introduce a lower bound for the number of linearly independent summable-square solutions of the discrete equation. Finally, we provide a limit-point criterion.
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Ugurlu, Ekin/0000-0002-0540-8545
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Keywords
Discrete Equations, Hamiltonian Systems, Sylvester'S Inertia Indices, Subspace Theory, Weyl'S Theory, 34B20, Weyl’s Theory, Sylvester’s Inertia Indices, 37J06, 46C07, Numerical Analysis, Symplectic Methods, Linear subspace, Mathematical optimization, Pure mathematics, Spectral Theory of Differential Operators, Discrete mathematics, Mathematical analysis, Hamiltonian Systems, Computational Theory and Mathematics, Combinatorics, Physical Sciences, Computer Science, Numerical Integration Methods for Differential Equations, FOS: Mathematics, Hamiltonian system, Mathematical Physics, Mathematics, Matrix Algorithms and Iterative Methods, Hamiltonian (control theory), Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators, Weyl theory and its generalizations for ordinary differential equations, discrete equations, Hamiltonian systems, Weyl's theory, Sylvester's inertia indices, subspace theory, Discrete version of topics in analysis
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01 natural sciences, 0101 mathematics
Citation
Uğurlu, Ekin; Bairamov, Elgiz (2024). "On the Maximal Subspaces of Discrete Hamiltonian Systems", Bulletin of the Malaysian Mathematical Sciences Society, Vol. 47, No. 3.
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3
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