Discrete Left-Definite Hamiltonian Systems
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Abstract
In this paper we consider an even-dimensional discrete Hamiltonian system on the set of nonnegative integers in the left-definite form. Using the inertia indices of the hermitian form related with the solutions of the equation we construct some maximal subspaces of the solution space. After constructing some ellipsoids preserving nesting properties we introduce a lower bound for the number of Dirichlet-summable solutions of the equation. Moreover we introduce a limit-point criterion.
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Keywords
Discrete Hamiltonian System, Weyl Theory, Left-Definite Equation, Sylvester'S Inertia Indices, Subspace Theory, Sylvester’s Inertia Indices, Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems, subspace theory, Difference and functional equations, General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants, discrete Hamiltonian system, Weyl theory, left-definite equation, Sylvester's inertia indices
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Citation
Uğurlu, E. (2023). "Discrete left-definite hamiltonian systems", Journal of Applied Analysis and Computation, Vol.13, No.3, pp.1178-1189.
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OpenCitations Citation Count
1
Volume
13
Issue
3
Start Page
1178
End Page
1189
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Scopus : 4
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4
checked on May 29, 2026
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4
checked on May 29, 2026
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