Separation problem for sturm-liouville equation with operator coefficient

Authors

  • Z. Oer Yildiz Technical University.

DOI:

https://doi.org/10.4067/S0716-09172001000200003

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

Z 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.

Author Biography

Z. Oer, Yildiz Technical University.

Department of Mathematics, Faculty of Art and Science.

References

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Published

2017-04-24

How to Cite

[1]
Z. Oer, “Separation problem for sturm-liouville equation with operator coefficient”, Proyecciones (Antofagasta, On line), vol. 20, no. 2, pp. 177-191, Apr. 2017.

Issue

Vol. 20 No. 2 (2001)

Section

Artículos
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