Geodesic
Carleson series of resonances in the Regge problem
Izvestiya. Mathematics , Tome 12 (1978) no. 1, pp. 21-51

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The scattering problem is investigated for a ystem of differential equations $-y''=k^2Ay$ on the interval $[0,a]$, where $A$ is a positive matrix-valued function which jumps to 1 for $x>a$. The scattering matrix for large spectral parameter is studied, the system of resonances is described, and an expression for the resonance states in terms of the Jost solution is given. A relation is established between the resonances and the poles of the analytic continuation of the Green function. It is proved that the syrtem of resonance states corresponding to complex zeros of the scattering matrix has serial structure; namely, it splits into $n$ Carleson series. The completeness of the system of resonances is investigated, and it is established that this system forms a Riesz basis in the corresponding space with the energy metric. Bibliography: 23 titles. 
@article{IM2_1978_12_1_a1,
     author = {S. A. Ivanov and B. S. Pavlov},
     title = {Carleson series of resonances in the {Regge} problem},
     journal = {Izvestiya. Mathematics },
     pages = {21--51},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {1978},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1978_12_1_a1/}
}
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S. A. Ivanov; B. S. Pavlov. Carleson series of resonances in the Regge problem. Izvestiya. Mathematics , Tome 12 (1978) no. 1, pp. 21-51. http://geodesic.mathdoc.fr/item/IM2_1978_12_1_a1/