A first order trace formula is obtained for a regular differential operator perturbed by a finite signed measure multiplication operator. ∞ N=1 . In what follows
We obtain a first-order trace formula for a higher order differential operator on a closed interval in the case where the perturbation operator is the operator of multiplication by a finite complex-valued charge. For operators of even orders
, the result contains a term of new type, previously unknown.
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A first order trace formula is obtained for a higher-order differential operator on a segment in the case where the perturbation is an operator of multiplication by a finite complex-valued measure. For the operators of even order n ≥ 4 a new term in the final formula is discovered.
В работе получена формула регуляризованного следа для дифференциального оператора высокого порядка на отрезке при возмущении младшего коэффициента конечным зарядом. Рассмотрены произвольные регулярные краевые условия и произвольный порядок оператора $n\geqslant 3$. Обнаружен новый эффект: при четном порядке оператора появляется дополнительное слагаемое, учитывающее скачок функции распределения заряда в середине отрезка.
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