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Quadratic functionals: positivity, oscillation, Rayleigh's principle
Archivum mathematicum, Tome 34 (1998) no. 1, pp. 143-151 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper we give a survey on the theory of quadratic functionals. Particularly the relationships between positive definiteness and the asymptotic behaviour of Riccati matrix differential equations, and between the oscillation properties of linear Hamiltonian systems and Rayleigh’s principle are demonstrated. Moreover, the main tools form control theory (as e.g. characterization of strong observability), from the calculus of variations (as e.g. field theory and Picone’s identity), and from matrix analysis (as e.g. l’Hospital’s rule for matrices) are discussed.
In this paper we give a survey on the theory of quadratic functionals. Particularly the relationships between positive definiteness and the asymptotic behaviour of Riccati matrix differential equations, and between the oscillation properties of linear Hamiltonian systems and Rayleigh’s principle are demonstrated. Moreover, the main tools form control theory (as e.g. characterization of strong observability), from the calculus of variations (as e.g. field theory and Picone’s identity), and from matrix analysis (as e.g. l’Hospital’s rule for matrices) are discussed.
Classification : 34C10, 34H05, 49K15, 49N10, 93B07, 93C05, 93C15
Keywords: Quadratic functional; Hamiltonian system; Riccati equation; oscillation; observability; Rayleigh’s principle; eigenvalue problem; linear control system 
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Kratz, Werner. Quadratic functionals: positivity, oscillation, Rayleigh's principle. Archivum mathematicum, Tome 34 (1998) no. 1, pp. 143-151. http://geodesic.mathdoc.fr/item/ARM_1998_34_1_a13/

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