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