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Inverse problems associated to a canonical differential system. (English) Zbl 0991.34070
Kérchy, László (ed.) et al., Recent advances in operator theory and related topics. The Béla Szőkefalvi-Nagy memorial volume. Proceedings of the memorial conference, Szeged, Hungary, August 2-6, 1999. Basel: Birkhäuser. Oper. Theory, Adv. Appl. 127, 1-27 (2001).

The authors deal with the canonical differential system

-iJf ' (t,λ)=λf(t,λ)+V(t)f(t,λ),t0,


J=I n 00-I n ,V(t)=0k(t)k(t) * 0,

and k(t), called the potential, is an n×n-matrix with entries in L 1 (0,). The authors provide a solution to the inverse problem of recovering k(t) from spectral characteristics in the particular case of strictly pseudo-exponential potentials.

34L25Scattering theory, inverse scattering (ODE)
34A55Inverse problems of ODE
81U40Inverse scattering problems (quantum theory)
47A56Functions whose values are linear operators
34B20Weyl theory and its generalizations