Abstract
A linear ordinary differential operator of first order with bounded coefficients is shown to be invertible in L n2 (−∞,∞) or Fredholm in L n2 (0,∞) if and only if the underlying system of homogeneous differential equations has a dichotomy. In that case the operator is proved to be a direct sum of two generators of C 0-semigroups, one of which has support on the negative half line and the other on the positive half line.
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Ben-Artzi, A., Gohberg, I. (1992). Dichotomy of Systems and Invertibility of Linear Ordinary Differential Operators. In: Gohberg, I. (eds) Time-Variant Systems and Interpolation. Operator Theory: Advances and Applications, vol 56. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8615-4_3
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DOI: https://doi.org/10.1007/978-3-0348-8615-4_3
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