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The Darlington Synthesis Problem

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Finite Blaschke Products and Their Connections

Abstract

The (scalar-valued) Darlington synthesis problem from electrical network theory asks the following question. Given a ∈ H , do there exist b, c, d ∈ H such that the matrix-valued analytic function

$$\displaystyle U = \begin {bmatrix} a & -b \\ c & d \end {bmatrix} $$

is unitary almost everywhere on \(\mathbb {T}\)?

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References

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Correspondence to Stephan Ramon Garcia , Javad Mashreghi or William T. Ross .

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Garcia, S.R., Mashreghi, J., Ross, W.T. (2018). The Darlington Synthesis Problem. In: Finite Blaschke Products and Their Connections. Springer, Cham. https://doi.org/10.1007/978-3-319-78247-8_13

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