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

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{10_21136_MB_2003_134182,
     author = {Do\v{s}l\'a, Zuzana and \v{S}krab\'akov\'a, Denisa},
     title = {Phases of linear difference equations and symplectic systems},
     journal = {Mathematica Bohemica},
     pages = {293--308},
     publisher = {mathdoc},
     volume = {128},
     number = {3},
     year = {2003},
     doi = {10.21136/MB.2003.134182},
     mrnumber = {2012606},
     zbl = {1055.39026},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2003.134182/}
}
TY  - JOUR
AU  - Došlá, Zuzana
AU  - Škrabáková, Denisa
TI  - Phases of linear difference equations and symplectic systems
JO  - Mathematica Bohemica
PY  - 2003
SP  - 293
EP  - 308
VL  - 128
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2003.134182/
DO  - 10.21136/MB.2003.134182
LA  - en
ID  - 10_21136_MB_2003_134182
ER  - 
%0 Journal Article
%A Došlá, Zuzana
%A Škrabáková, Denisa
%T Phases of linear difference equations and symplectic systems
%J Mathematica Bohemica
%D 2003
%P 293-308
%V 128
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2003.134182/
%R 10.21136/MB.2003.134182
%G en
%F 10_21136_MB_2003_134182
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. http://geodesic.mathdoc.fr/articles/10.21136/MB.2003.134182/

Cité par Sources :