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Global representations of the kernel of the resolvent of a non-self-adjoint operator in the Keldysh sense. (English. Russian original) Zbl 0957.47002
Russ. Math. Surv. 51, No. 3, 545-546 (1996); translation from Usp. Mat. Nauk 51, No. 3, 199-200 (1996).
The author studies the kernel of the resolvent of a sum \(T+P\) of a lower semibounded discrete operator \(T\) in \(L^2(D)\), \(D\) kompact in \(\mathbb{R}^N\), \(N\geq 1\), and a bounded operator \(P\) in \(L^2(D)\). He proves a representation of this kernel as a sum of partial fractions expressed in terms of Keldysh systems of eigenvectors and adjoint vectors of \(T+P\) and \(T+ P^*\).
MSC:
47A10 Spectrum, resolvent
47A70 (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces
47B38 Linear operators on function spaces (general)
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