## Proyecciones (Antofagasta)

*Print version* ISSN 0716-0917

#### Abstract

OER, Z.. SEPARATION PROBLEM FOR STURM-LIOUVILLE EQUATION WITH OPERATOR COEFFICIENT.* Proyecciones (Antofagasta)* [online]. 2001, vol.20, n.2, pp.177-191.
ISSN 0716-0917. http://dx.doi.org/10.4067/S0716-09172001000200003.

*Let H be a separable Hilbert Space. Denote by H _{1} = L_{2}(a,b; H)*

*the set of function defned on the interval a*< c < b (¾¥ a < c < b £¥)

*whose values belong to H strongly measurable [12] and satisfying the condition*

*If the inner product of function*¦(c)

*and g*(c)

*belonging to H*

_{1 }

*is defined by*

*then H*

_{1 }

*forms a separable Hilbert space. We study separation problem for the operator formed*

*by*¾

*y"+ Q*(c)

*y Sturm-Liouville differential expression in L*

_{2}

*(¾ ¥, ¥; H) space has been proved where*

*Q*(c)

*in an operator which transforms at H in value of c,,self-adjoint, lower bounded and its inverse is complete continous*