On the integral manifold of a nonlinear system in a Hilbert space

1968 ◽  
pp. 117-130
Author(s):  
Ju. A. Mitropol′skiĭ ◽  
O. B. Lykova
Keyword(s):  
Hilbert Space ◽  
Nonlinear System ◽  
Integral Manifold

scholarly journals Feedback Systems on Extended Hilbert Space-Normality and Linearization

2020 ◽  
Vol 12 (2) ◽  
pp. 28
Author(s):  
Messaoudi Khelifa
Keyword(s):  
Hilbert Space ◽  
Nonlinear System ◽  
Feedback Systems

ThestudyofthenormalityofafeedbacksystemonanextendedHilbertspacehasbeenmade. Theresultsofapproximation of the solutions of such a nonlinear system by another linear are also established. This study represents an extension of the work of (Vaclav Dolezal, 1979), on a Hilbert space.

scholarly journals A general framework for quantum splines

2018 ◽  
Vol 15 (09) ◽  
pp. 1850147 ◽  
Author(s):  
L. Abrunheiro ◽  
M. Camarinha ◽  
J. Clemente-Gallardo ◽  
J. C. Cuchí ◽  
P. Santos
Keyword(s):  
Optimal Control ◽  
Hilbert Space ◽  
Quantum Mechanics ◽  
Nonlinear System ◽  
General Framework ◽  
Hamiltonian Approach ◽  
Density Matrices ◽  
Quantum Domain ◽  
Riemannian Cubic ◽  
Geometrical Formulation

Quantum splines are curves in a Hilbert space or, equivalently, in the corresponding Hilbert projective space, which generalize the notion of Riemannian cubic splines to the quantum domain. In this paper, we present a generalization of this concept to general density matrices with a Hamiltonian approach and using a geometrical formulation of quantum mechanics. Our main goal is to formulate an optimal control problem for a nonlinear system on [Formula: see text] which corresponds to the variational problem of quantum splines. The corresponding Hamiltonian equations and interpolation conditions are derived. The results are illustrated with some examples and the corresponding quantum splines are computed with the implementation of a suitable iterative algorithm.

Hilbert Space

1993 ◽  
Author(s):  
J. R. Retherford
Keyword(s):  
Hilbert Space
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