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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

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Volume 23, Issue 3


A spectral representation of the linear multivelocity transport problem

Mariam Avalishvili / Dazmir Shulaia
  • I. Vekua Institute of Applied Mathematics, I. Javakhishvili Tbilisi State University, 2 University Str., Tbilisi 0186; and Georgian Technical University, 77 Kostava Str.,Tbilisi 0175, Georgia
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Published Online: 2016-08-18 | DOI: https://doi.org/10.1515/gmj-2016-0033


The transformation of the original characteristic equation of the multivelocity linear transport theory was carried out by expanding the scattering function for the problem to be solved as a spectral integral over a complete set of eigenfunctions for the previously solved transport problem. The obtained equation represents a singular integral equation containing a spectral integral over the spectrum of the solved problem, whose kernel depends on the difference between the scattering of the problem to be solved and that of the already solved problem. We consider also the examples illustrating the validity of such a transformation. M. Kanal and J. Davies made a similar transformation of the characteristic equation of the one-velocity transport theory.

Keywords: Spectral integral; eigenfunctions; eigenvalues; inverse problem

MSC 2010: 45A05; 82D75; 45E99; 11F72


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About the article

Received: 2014-12-29

Accepted: 2015-04-14

Published Online: 2016-08-18

Published in Print: 2016-09-01

Citation Information: Georgian Mathematical Journal, Volume 23, Issue 3, Pages 329–341, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2016-0033.

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