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Creators/Authors contains: "Tully-Doyle, Ryan"

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  1. ; (, Results in Mathematics)
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  2. ; (, Advances in Mathematics)
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  3. ; (, Linear Algebra and its Applications)
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  4. ; ; (, International Mathematics Research Notices)
    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. 
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  5. ; (, Annales Polonici Mathematici)
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