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 conditionZ b a ||f(x)||2 Hdx < ? If the inner product of function ¦(c) and g(c) belonging to H1 is defined by (f, g)1 = Z b a (f(x), g(x))Hdx 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.
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