A Generalized Index Theorem for Monotone Matrix-Valued Functions with Applications to Discrete Oscillation Theory

DOI10.1137/120873029zbMath1365.39009OpenAlexW2027365936MaRDI QIDQ5300553

Werner Kratz, Roman Šimon Hilscher

Publication date: 27 June 2013

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/7a79e9efd1e31d963f0f4d686107f39523592bf0

zbMATH Keywords

limit theoremSturm-Liouville difference equationindex theoremoscillation theoremdiscrete symplectic systemrank theorem

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Hermitian, skew-Hermitian, and related matrices (15B57) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Monotonic functions, generalizations (26A48) Oscillation theory for difference equations (39A21)

Related Items (8)

Relative oscillation theory for matrix Sturm-Liouville difference equations extended ⋮ Oscillation numbers for continuous Lagrangian paths and Maslov index ⋮ Generalized oscillation theorems for symplectic difference systems with nonlinear dependence on spectral parameter ⋮ Renormalized oscillation theory for symplectic eigenvalue problems with nonlinear dependence on the spectral parameter ⋮ Recessive solutions for nonoscillatory discrete symplectic systems ⋮ Eigenvalue theory for time scale symplectic systems depending nonlinearly on spectral parameter ⋮ Discrete oscillation theorems for symplectic eigenvalue problems with general boundary conditions depending nonlinearly on spectral parameter ⋮ Discrete oscillation theorems and weighted focal points for Hamiltonian difference systems with nonlinear dependence on a spectral parameter

This page was built for publication: A Generalized Index Theorem for Monotone Matrix-Valued Functions with Applications to Discrete Oscillation Theory