# Quadratic functionals: positivity, oscillation, Rayleigh's principle

Archivum Mathematicum (1998)

- Volume: 034, Issue: 1, page 143-151
- ISSN: 0044-8753

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topKratz, Werner. "Quadratic functionals: positivity, oscillation, Rayleigh's principle." Archivum Mathematicum 034.1 (1998): 143-151. <http://eudml.org/doc/248207>.

@article{Kratz1998,

abstract = {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.},

author = {Kratz, Werner},

journal = {Archivum Mathematicum},

keywords = {Quadratic functional; Hamiltonian system; Riccati equation; oscillation; observability; Rayleigh’s principle; eigenvalue problem; linear control system; quadratic functional; Hamiltonian system; Riccati equation; oscillation; Rayleigh's principle; eigenvalue problem; linear control system; observability},

language = {eng},

number = {1},

pages = {143-151},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Quadratic functionals: positivity, oscillation, Rayleigh's principle},

url = {http://eudml.org/doc/248207},

volume = {034},

year = {1998},

}

TY - JOUR

AU - Kratz, Werner

TI - Quadratic functionals: positivity, oscillation, Rayleigh's principle

JO - Archivum Mathematicum

PY - 1998

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 034

IS - 1

SP - 143

EP - 151

AB - 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.

LA - eng

KW - Quadratic functional; Hamiltonian system; Riccati equation; oscillation; observability; Rayleigh’s principle; eigenvalue problem; linear control system; quadratic functional; Hamiltonian system; Riccati equation; oscillation; Rayleigh's principle; eigenvalue problem; linear control system; observability

UR - http://eudml.org/doc/248207

ER -

## References

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