Commuting nonselfadjoint operators and algebraic curves Academic Article uri icon

abstract

  • As was discovered by M.S.Livsic, methods of algebraic geometry play an important role in the theory of commuting nonselfadjoint operators. Using further geometrical ideas, we construct triangular models for pairs of commuting nonselfadjoint operators with finite-dimensional imaginary parts and a smooth discriminant curve. The characteristic function of a pair of commuting nonselfadjoint operators turns out to be a function on the discriminant curve, and the reduction of the pair of operators to the triangular model corresponds to the canonical factorization for semicontractive functions on a compact real Riemann surface.

publication date

  • January 1, 1992