Constrained optimization and analytic spectral factorization

TL;DRAbstract

Let [special characters omitted] be function of [special characters omitted], 0 [special characters omitted], and [special characters omitted], that takes m x m nonnegative matrix values and such that [special characters omitted] for all [special characters omitted]) and all [special characters omitted]. Denote by [special characters omitted] the space of N-vector valued functions continuous on the closed unit disc in [special characters omitted] and analytic inside the disc whose Taylor series expansion about 0 has real coefficients. We consider the following problem: [special characters omitted]where [special characters omitted] is a subset of [special characters omitted] that may depend on given continuous N-vector valued functions [special characters omitted] whose entries have real Fourier coefficients, on given continuous scalar valued functions [special characters omitted] with real Fourier coefficients, and on given real constants cl. The set [special characters omitted] we con

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