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Journal of the London Mathematical Society (1)

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THE $2\times 2$ SPECTRAL NEVANLINNA–PICK PROBLEM
CONSTANTIN COSTARA
Journal:

Journal of the London Mathematical Society / Volume 71 / Issue 3 / June 2005

Published online by Cambridge University Press:

24 May 2005, pp. 684-702

Print publication:

June 2005
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A method is presented to construct interpolation functions into the $2\times 2$ open spectral unit ball. For the spectral Nevanlinna–Pick problem, these functions are in some sense extremal, and the set of all these interpolation functions is enough to solve any interpolation problem, with solvable finite interpolation data. This fact is used to compute the complex geodesics for the symmetrized bidisc and for the spectral unit ball, and to solve completely the two-point interpolation problem for the two target sets.