The main object described is a general theory of self-adjoint eigenvalue problems for linear Hamiltonian systems, which includes Morse's oscillation theory and his extensions of Sturmian theory. The dependence of the eigenvalue parameter may be nonlinear. The treatment is based upon a novel approach via field theory, in particular Picone's theory. The central features needed for the method are results on Riccati matrix differential equations and on monotone matrix-values functions. Applications of the theory yield classical and differing results in such areas as for example, linear control theory, variational analysis (Rayleigh's principle) or Sturm-Liouville eigenvalue problems.
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
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Gewicht
ISBN-13
978-3-05-501656-1 (9783055016561)
Schweitzer Klassifikation
Part 1 Self-adjoint linear differential systems: Picone's identity; disconjugacy; oscillation. Part 2 Riccati matrix differential equations: inequalities; index results; asymptotics. Part 3 Matrix analysis: oscillatory and asymptotic behaviour of monotone matrix-valued functions. Part 4 Topics in linear control theory: controllability and strong observability; construction of observers; canonical forms; arbitary pole assignment. Part 5 Self-adjoint eigenvalue problems for linear Hamiltonian systems: oscillation; Sturmian theory; comparison and existence of eigenvlaues; Rayleigh's principle; expansion theorems. Part 6 Applications: the optimal linear regulator and Rayleigh's principle; Sturm-Liouville and Kamke eigenvalue problems; nonnegativity of quadratic functionals; variational principles. (Part contents).
