Abstract
We consider the bitangential Nevanlinna-Pick problem for meromorphic matrix functions with upper bounded total pole multiplicity. We follow the approach of J.A. Ball and J.W. Helton to view this problem as a shift invariant maximal semi-definite sub-space problem in a space with indefinite inner product. The abstract problem to be solved is a slightly modified version of the generalized interpolation problem for matrix valued functions, considered by Ball and Helton. Using a generalization of a theorem of I.S. Iokhvidov on the existence of invariant maximal semi-definite subspaces, the meromorphic case of the generalized interpolation problem is solved, and it is shown that this contains the bitangential Nevanlinna-Pick problem with poles.
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Gheondea, A. (1998). On generalized interpolation and shift invariant maximal semidefinite subspaces. In: Gohberg, I., Mennicken, R., Tretter, C. (eds) Recent Progress in Operator Theory. Operator Theory Advances and Applications, vol 103. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8793-9_7
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DOI: https://doi.org/10.1007/978-3-0348-8793-9_7
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