Displaying similar documents to “Boundary problems for generalized Lyapunov equations.”

Integral equations and time varying linear systems.

Lucas Jódar (1986)

Stochastica

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In this paper we study the resolution problem of an integral equation with operator valued kernel. We prove the equivalence between this equation and certain time varying linear operator system. Sufficient conditions for solving the problem and explicit expressions of the solutions are given.

Algebraic methods for solving boundary value problems.

Lucas Jódar Sánchez (1986)

Stochastica

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By means of the reduction of boundary value problems to algebraic ones, conditions for the existence of solutions and explicit expressions of them are obtained. These boundary value problems are related to the second order operator differential equation X + AX + AX = 0, and X = A + BX + XC. For the finite-dimensional case, computable expressions of the solutions are given.

Representation of continuous associative functions.

Barbara Baccheli (1986)

Stochastica

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Strengthened forms of Ling's representation theorem concerning a class of continuous associative functions are given: Firstly the monotonicity condition is removed. Then the associativity condition is replaced by the power associativity.

Some remarks on a problem of C. Alsina.

J. Matkowski, M. Sablik (1986)

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Equation [1] f(x+y) + f (f(x)+f(y)) = f (f(x+f(y)) + f(f(x)+y)) has been proposed by C. Alsina in the class of continuous and decreasing involutions of (0,+∞). General solution of [1] is not known yet. Nevertheless we give solutions of the following equations which may be derived from [1]: [2] f(x+1) + f (f(x)+1) = 1, [3] f(2x) + f(2f(x)) = f(2f(x + f(x))). Equation [3] leads to a Cauchy functional equation: ...

Weighted shift operators on l spaces.

Lucas Jódar (1986)

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The analytic-spectral structure of the commutant of a weighted shift operator defined on a l space (1 ≤ p < ∞) is studied. The cases unilateral, bilateral and quasinilpotent are treated. We apply the results to study certain questions related to unicellularity, strictly cyclicity and the existence of hyperinvariant subspaces.

On the extension of Rosenbrock's theory in algebraic design on multivariable controllers.

Manuel de la Sen (1986)

Stochastica

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System similarity and system strict equivalence concepts from Rosenbrock's theory on linear systems are used to establish algebraic conditions of model matching as well as an algebraic method for design of centralized compensators. The ideas seem to be extensible without difficulty to a class of decentralized control.