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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.20 n.2 Antofagasta ago. 2001

http://dx.doi.org/10.4067/S0716-09172001000200003 

SEPARATION PROBLEM FOR
STURM-LIOUVILLE EQUATION
WITH OPERATOR COEFFICIENT

Z. OER

Yildiz Technical University, Turkey

Abstract

Let H be a separable Hilbert Space. Denote by H1 = L2(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 H1 is defined by


then H1 forms a separable Hilbert space. We study separation problem for the operator formed by ¾ y"+ Q (c) y Sturm-Liouville differential expression in L2(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.

 

References

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Received : July 2000.

Z. OER

Departmet of Mathematics

Faculty of Art and Science

Yildiz Technical University

34210, Davutpasa

Istanbul

Turkey

E- MAIL : zoer@yildiz.edu.tr