Discrete Dynamics in Nature and Society
Volume 2004 (2004), Issue 1, Pages 221-249

Spectral analysis for a class of integral-difference operators: known facts, new results, and open problems

Yuri B. Melnikov

International Solvay Institutes for Physics and Chemistry, Campus Plain ULB, C.P. 231, Boulevard du Triomphe, Brussels 1050, Belgium

Received 5 January 2004

Copyright © 2004 Yuri B. Melnikov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present state of the art, the new results, and discuss open problems in the field of spectral analysis for a class of integral-difference operators appearing in some nonequilibrium statistical physics models as collision operators. The author dedicates this work to the memory of Professor Ilya Prigogine, who initiated this activity in 1997 and whose interesting and most enlightening advices had gudided the author during all these years.