Explicit Solutions of Two-Point Boundary Value Operator Problems.
Decomposition of operators with countable spectrum.
Sufficient spectral conditions for the existence of a spectral decomposition of an operator T defined on a Banach space X, with countable spectrum, are given. We apply the results to obtain the West decomposition of certain Riesz operators.
On strictly cyclic operator algebras.
In the present paper we prove that a strictly cyclic, not invertible unicellular operator is quasinilpotent.
Sobre los operadores desplazamiento ponderados sub-acotados.
We study the relation between the sets of cyclic vectors of an unilateral bounded below weighted shift operator T and T where S is an invariant subspace of T. It is proved that T can not be unicellular and known results are generalized.
Integral equations and time varying linear systems.
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.
Sobre los operadores desplazamiento bilateral ponderados e invertibles.
In this paper the analytic-spectral structure of the commutant of an invertible bilateral weighted shift operator is studied, extending known results. A class of operators is introduced, more general than the class of the rationally strictly cyclic bilateral shift [operators] which are not unicellular.
Subespacios hiperinvariantes de operadores desplazamiento bilateral con sucesiones de pesos convergentes: {w}, {w}, n = 1, ..., ∞.
Estudiamos la existencia de subespacios hiperinvariantes de operadores desplazamiento bilateral ponderados e invertibles definidos sobre un espacio de Hilbert con base ortogonal {e}, n perteneciendo a Z, por la expresión T e = w e, donde las sucesiones {w} y {w}, con n = 1, ..., ∞, son convergentes.
Weighted shift operators on l spaces.
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.
Una nota sobre cuasinilpotencia y unicelularidad de los operadores desplazamiento ponderados.
In this paper a class of injective unilateral weighted shift operators is introduced which contains strictly the class of the strictly cyclic operators and which can only be unicellular if they are quasinilpotent.
Operadores desplazamiento condicionalmente estrictamente cíclicos.
Sobre la estructura analítica de operadores desplazamiento cuasinilpotentes.
Una nota sobre la descomposición espectral de operadores acotados.
Boundary value problems for coupled systems of second order differential equations with a singularity of the first kind: explicit solutions
In this paper we obtain existence conditions and an explicit closed form expression of the general solution of twopoint boundary value problems for coupled systems of second order differential equations with a singularity of the first kind. The approach is algebraic and is based on a matrix representation of the system as a second order Euler matrix differential equation that avoids the increase of the problem dimension derived from the standard reduction of the order method.
Explicit solutions for Sturm-Liouville operator problems (II).
It is proved that the resolution problem of a Sturm-Liouville operator problem for a second-order differential operator equation with constant coefficients is solved in terms of solutions of the corresponding algebraic operator equation. Existence and uniqueness conditions for the existence of nontrivial solutions of the problem and explicit expressions of them are given.
Algebraic methods for solving boundary value problems.
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.
Boundary problems for generalized Lyapunov equations.
Boundary value problems for generalized Lyapunov equations whose coefficients are time-dependant bounded linear operators defined on a separable complex Hilbert space are studied. Necessary and sufficient conditions for the existence of solutions and explicit expressions of them are given.
Singular bilateral boundary value problems for discrete generalized Lyapunov matrix equations.
Existence and uniqueness conditions for solving singular initial and two-point boundary value problems for discrete generalized Lyapunov matrix equations and explicit expressions of solutions are given.
Explicit solutions for non homogeneous Sturm-Liouville operators problems.
In this paper we study existence and sufficiency conditions for the solutions of Sturm-Liouville operator problems related to the operator differential equation X'' - QX = F(t). Explicit solutions of the problem in terms of a square root of the operator Q are given.
Sobre la ecuación cuadrática en operadores A + BT +TC + TDT = 0.
By means of the application of annihilating entire functions of an operator, the bilateral quadratic equation in operators A + BT +TC + TDT = 0, is changed into an unilateral linear equation, obtaining conditions under which the solutions of such linear equation satisfy the quadratic equation.
Bessel matrix differential equations: explicit solutions of initial and two-point boundary value problems
In this paper we consider Bessel equations of the type , where A is an nn complex matrix and X(t) is an nm matrix for t > 0. Following the ideas of the scalar case we introduce the concept of a fundamental set of solutions for the above equation expressed in terms of the data dimension. This concept allows us to give an explicit closed form solution of initial and two-point boundary value problems related to the Bessel equation.
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