Další formáty:
BibTeX
LaTeX
RIS
@article{822194,
author = {Bohner, Martin and Došlý, Ondřej and Kratz, Werner},
article_number = {6},
keywords = {Discrete symplectic system; discrete quadratic functional; Rayleigh principle; extended Picone identity},
language = {eng},
issn = {0002-9947},
journal = {Trans. Amer. Math. Soc.},
title = {Sturmian and spectral theory for discrete symplectic systems},
url = {http://www.ams.org/tran/2009-361-06},
volume = {361},
year = {2009}
}
TY - JOUR
ID - 822194
AU - Bohner, Martin - Došlý, Ondřej - Kratz, Werner
PY - 2009
TI - Sturmian and spectral theory for discrete symplectic systems
JF - Trans. Amer. Math. Soc.
VL - 361
IS - 6
SP - 3109-3123
EP - 3109-3123
SN - 00029947
KW - Discrete symplectic system
KW - discrete quadratic functional
KW - Rayleigh principle
KW - extended Picone identity
UR - http://www.ams.org/tran/2009-361-06
N2 - We consider symplectic difference systems together with associated discrete quadratic functionals and eigenvalue problems. We establish Sturmian type comparison theorems for the numbers of focal points of conjoined bases of a pair of symplectic systems. Then, using this comparison result, we show that the numbers of focal points of two conjoined bases of one symplectic system differ by at most n. In the last part of the paper we prove the Rayleigh principle for symplectic eigenvalue problems and we show that finite eigenvectors of such eigenvalue problems form a complete orthogonal basis in the space of admissible sequences.
ER -
BOHNER, Martin, Ondřej DOŠLÝ a Werner KRATZ. Sturmian and spectral theory for discrete symplectic systems. \textit{Trans. Amer. Math. Soc.}. 2009, roč.~361, č.~6, s.~3109-3123. ISSN~0002-9947.
|
