Geodesic
Phases of linear difference equations and symplectic systems
Mathematica Bohemica, Tome 128 (2003) no. 3, pp. 293-308

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The second order linear difference equation \[ \Delta (r_k\triangle x_k)+c_kx_{k+1}=0, \qquad \mathrm{(1)}\] where $r_k\ne 0$ and $k\in \mathbb{Z}$, is considered as a special type of symplectic systems. The concept of the phase for symplectic systems is introduced as the discrete analogy of the Borůvka concept of the phase for second order linear differential equations. Oscillation and nonoscillation of (1) and of symplectic systems are investigated in connection with phases and trigonometric systems. Some applications to summation of number series are given, too.
The second order linear difference equation \[ \Delta (r_k\triangle x_k)+c_kx_{k+1}=0, \qquad \mathrm{(1)}\] where $r_k\ne 0$ and $k\in \mathbb{Z}$, is considered as a special type of symplectic systems. The concept of the phase for symplectic systems is introduced as the discrete analogy of the Borůvka concept of the phase for second order linear differential equations. Oscillation and nonoscillation of (1) and of symplectic systems are investigated in connection with phases and trigonometric systems. Some applications to summation of number series are given, too.
DOI : 10.21136/MB.2003.134182
Classification : 39A05, 39A10, 39A11, 39A12
Keywords: second order linear difference equation; symplectic system; phase; oscillation; nonoscillation; trigonometric transformation 
Došlá, Zuzana; Škrabáková, Denisa. Phases of linear difference equations and symplectic systems. Mathematica Bohemica, Tome 128 (2003) no. 3, pp. 293-308. doi: 10.21136/MB.2003.134182
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