zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Disconjugacy for linear Hamiltonian difference systems. (English) Zbl 0762.39003
Using Riccati methods, disconjugacy criteria are obtained for the linear Hamiltonian difference system (1) $\Delta y(t)=B(t)y(t+1)+C(t)z(t)$, $\Delta z(t)=-A(t)y(t+1)-B\sp*(t)z(t)$, where $\Delta y(t)=y(t+1)-y(t)$, $A,C$ are $d\times d$ Hermitian matrices and $B$ is a $d\times d$ matrix such that $I-B$ and $C$ are regular. Here (1) is said to be disconjugate on $[M-1,N+1]$ if there exists at most one integer $p\in[M-1,N]$ such that $y\sp*(p)C\sp{-1}(p)(I-B(p))y(p+1)\le 0$ for any nontrivial solution $y(t)$, $z(t)$ of (1).
Reviewer: H.Länger (Wien)

39A10Additive difference equations
39A12Discrete version of topics in analysis
Full Text: DOI
[1] Ahlbrandt, C.; Hooker, J.: Recessive solutions of symmetric three term recurrence relations. Canad. math. Soc., conference proceeding 8, 3-42 (1987)
[2] Ahlbrandt, C.; Hooker, J.: Riccati matrix difference equations and disconjugacy of discrete linear systems. SIAM J. Math. anal. 19, 1183-1197 (1988) · Zbl 0655.39001
[3] Coppel, W. A.: Disconjugacy. Lecture notes in mathematics, 34-80 (1971)
[4] Chen, S.; Erbe, L.: Riccati techniques and discrete oscillations. J. math. Anal. appl. 142, 468-487 (1989) · Zbl 0686.39001
[5] Chen, S.; Erbe, L.: Oscillation and nonoscillation for systems of self-adjoint second-order difference equations. SIAM J. Math. anal. 20, 939-949 (1989) · Zbl 0687.39001
[6] A. Peterson and J. Ridenhour, Disconjugacy for a second order system of difference equations, to appear. · Zbl 0731.39005