Trace formulas for compact perturbations of operators with discrete spectrum

Abstract

 ðàáîòå ïðèâîäèòñÿ íåîáõîäèìîå è äîñòàòî÷íîå óñëîâèå ðàâåíE ñòâà íóëþ ñóììû ðåãóëÿðèçîâàííîãî ñëåäà ñî ñêîáêàìè ñ âû÷åòîì ïåðâîé ïîïðàâêè òåîðèè âîçìóùåíèéF Êëþ÷åâûå ñëîâàX äèôôåðåíöèàëüíûå îïåðàòîðûD ñïåêòðD ôîðìóëà ñëåäîâFTrace formulas for compact perturbations of operators with discrete spectrum. We give the necessary and sufficient condition of vanishing of the regularized trace sum with first correction of the perturbation theory to be subtracted and with groupings.