Abstract
A characterization of the set of linear fractional transformations (ω 11ε+ ω12)(ω21ε+ ω22)-1,where the wij are the block entries of a j pq inner matrix-valued function and E runs over the set of p × q matrix-valued functions that are holomorphic and contractive in either the open unit disk or the open upper (or right) half-plane is derived. This formula leads to transparent proofs of a number of bitangential interpolation problems. The analysis uses methods based on the special class of reproducing kernel Hilbert spaces that were introduced and extensively studied by L. de Branges. Connections with Riccati equations are exploited.
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Dym, H. (2003). Linear Fractional Transformations, Riccati Equations and Bitangential Interpolation, Revisited. In: Alpay, D. (eds) Reproducing Kernel Spaces and Applications. Operator Theory: Advances and Applications, vol 143. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8077-0_6
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DOI: https://doi.org/10.1007/978-3-0348-8077-0_6
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