Discrete Dynamics in Nature and Society 
Volume 2004 (2004), Issue 1, Pages 221-249
doi:10.1155/S1026022604401022

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

Abstract

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.