01-211 Kuperin Yu., Naboko S., Romanov R.

Spectral analysis of transport operator: functional model approach (113K, 114K, LaTeX 2e ) Jun 5, 01

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Abstract. This paper presents the spectral analysis of the dissipative one-speed transport operator for the cases of a finite slab and of a finite body, by means of the Szokefalvi-Nagy - Foias functional model. It is shown that the essential spectrum of the operator is absolutely continuous with one possible spectral singularity at point $0$. The absolutely continuous component of the operator is studied in detail in the nontrivial case, when the spectral singularity does occur.

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