Spectral Analysis of the Transport Operator: A Functional Model Approach

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...

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Bibliographic Details
Published in:Indiana University mathematics journal 2002-01, Vol.51 (6), p.1389-1425
Main Authors: Kuperin, Yuri A., Nabokov, Serguei N., Romanov, Roman V.
Format: Article
Language:English
Subjects:
Continuous spectra
Eigenfunctions
Eigenvalues
Hilbert spaces
Mathematical functions
Mathematics
Scalar multiple
Spectral theory
Spectroscopic analysis
Spectroscopy
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Summary: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.
ISSN:0022-2518
1943-5258
DOI:10.1512/iumj.2002.51.2180