Discrete trigonometric and hyperbolic systems: An overview
Petr Zem\'anek
TL;DR
This paper provides an overview of discrete trigonometric and hyperbolic systems, highlighting their properties as discrete analogues of continuous systems and extending scalar formulas to n-dimensional cases.
Contribution
It offers a comprehensive overview of discrete trigonometric and hyperbolic systems, including their extensions to n-dimensional cases as analogues of continuous formulas.
Findings
Discrete systems mirror continuous trigonometric and hyperbolic properties.
Extensions to n-dimensional systems are established.
The overview consolidates key results in the field.
Abstract
In this paper we present an overview of results for discrete trigonometric and hyperbolic systems. These systems are discrete analogues of trigonometric and hyperbolic linear Hamiltonian systems. We show results which can be viewed as discrete n-dimensional extensions of scalar continuous trigonometric and hyperbolic formulas
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Quantum chaos and dynamical systems · Spectral Theory in Mathematical Physics