SPECTRAL ANALYSIS FOR A CLASS OF INTEGRAL-DIFFERENCE OPERATORS: KNOWN FACTS, NEW RESULTS, AND OPEN PROBLEMS

摘要

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 nonequi-librium 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.