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- W4225366144 abstract "Abstract In this paper, we give formulas that allow one to move between transfer function type realizations of multi-variate Schur, Herglotz, and Pick functions, without adding additional singularities except perhaps poles coming from the conformal transformation itself. In the two-variable commutative case, we use a canonical de Branges–Rovnyak model theory to obtain concrete realizations that analytically continue through the boundary for inner functions that are rational in one of the variables (so-called quasi-rational functions). We then establish a positive solution to McCarthy’s Champagne conjecture for local to global matrix monotonicity in the settings of both two-variable quasi-rational functions and $d$-variable perspective functions." @default.
- W4225366144 created "2022-05-05" @default.
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- W4225366144 date "2022-04-05" @default.
- W4225366144 modified "2023-09-26" @default.
- W4225366144 title "Analytic Continuation of Concrete Realizations and the McCarthy Champagne Conjecture" @default.
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- W4225366144 doi "https://doi.org/10.1093/imrn/rnac050" @default.
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