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K0 (AT ∗ M,π ) следующей C ∗ -алгебры (ср. ]) AT ∗ M,π = (u, v) u ∈ C0 (T (M \U )) , v ∈ C0 T ∗ Y , Endπ! 1. ], так как при Y = ∅ соответствующая K-группа есть Kc0 (T ∗ M )) и определена точная последовательность Kc1 (T ∗ (M \U )) → Kc0 (T ∗ Y ) → K0 (AT ∗ M,π ) → Kc0 (T ∗ (M \U )) → Kc1 (T ∗ Y ) . (9) — последовательность пары, отвечающая идеалу {(0, v) |v ∈ C0 (T Y, Endπ!

1 A−1 y = − (E + N1 )−1 P −1 (y ′ (x) + ay(x)), δ (4) 1 A(0, t)(E + N1 )−1 P −1 (y ′ (t) + ay(t))dt, y(0) = (5) 0 где P f (x) = (α1 −α2 )f (x)+(α3 −α4 )f (1−x), N1 – интегральный оператор, a – комплексная константа. ) к виду: γ1 y(0) + γ2 y(1) = (y, ϕ), (y, ϕ) – скалярное произведение, ϕ – непрерывная функция, N – такой оператор, что E + N = (E + N1 )−1 , E – единичный оператор. Построение резольвенты R0,λ сводится к исследованию краевой задачи для дифференциальной системы первого порядка в пространстве вектор-функций размерности 2.

20) 0 0 . 0 −i Тогда для регулярной струны с условием в правом конце вида f1 (l + 0) = 0 получим Положим B1 = dom(LS ) = dom(LB1 ) = {f ∈ dom(L∗ ) : Γ1 f = B1 Γ0 f }. (21) 28 Section 1. Spectral Problems Очевидно, что вектор–функция f (x, λ) является решением уравнения L∗0 y − λy = 0 в том и только том случае, когда она имеет вид c1 ψ(x, λ2 ) + c2 ϕ(x, λ2 ) i (c ψ ′ (x, λ2 ) + c2 ϕ′m (x, λ2 )) λ 1 m f (x, λ) = (22) . Пусть функция Вейля, соответствующая граничной тройке Π1 имеет вид M11 (λ) M12 (λ) M (λ) = .

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