The singularities of the $\mathcal{S}$-matrix and Green's function associated with perturbations of $ - \Delta$ acting in a cylinder
Charles Irwin Goldstein · Bulletin of the American Mathematical Society · 1973
It is the purpose of this note to study the singularities of the ^-matrix and Green's function associated with the operators considered in [l]-[3].As will be seen, there are a countable number of branch points, as well as a countable number of different ^-matrices associated with these operators.In this respect, these results differ considerably from those drawn from quantum mechanical scattering 2 and the exterior problem (see e.g.[4] and [5]).(1970).Primary 35J05, 35J10, 47A40, 78A50.Key words and phrases.Singularities of the ^-matrix, Green's function, waveguides, infinitely sheeted Riemann surface, analytic and meromorphic continuation, radiation condition, resonant state. AMS (MOS) subject classifications1 Work performed under the joint auspices of the Atomic Energy Commission and the Mathematics Research Center at the University of Wisconsin.2 Our results are related to wave progagation in a waveguide.3 We might just as easily consider the infinite cylinder, S' = (x = (3c, x N ) | x e /, -oo < x N < oo).