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Spectral analysis of dissipative Schrödinger operators

Published online by Cambridge University Press:  14 November 2011

B. P. Allahverdiev  and
Ahmet Canoǧlu
B. P. Allahverdiev
Affiliation:
Mathematics Department, Istanbul Technical University, 80626, Maslak, Istanbul, Turkey
Ahmet Canoǧlu
Affiliation:
Mathematics Department, Istanbul Technical University, 80626, Maslak, Istanbul, Turkey
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Extract

Dissipative Schrodinger operators are studied in L2(0, ∞) which are extensions of symmetric operators with defect index (2, 2). We construct a selfadjoint dilation and its incoming and outgoing spectral representations, which makes it possible to determine the scattering matrix according to the scheme of Lax and Phillips. With the help of the incoming spectral representation, we construct a functional model of the dissipative operator and construct its characteristic function in terms of solutions of the corresponding differential equation. On the basis of the results obtained regarding the theory of the characteristic function, we prove a theorem on completeness of the system of eigenfunctions and associated functions of the dissipative operator.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 6 , 1997 , pp. 1113 - 1121
Copyright
Copyright © Royal Society of Edinburgh 1997

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References

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