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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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