Characterizing matrix monotonicity of fixed order on general sets
classification
🧮 math.FA
keywords
matrixordercharacterizationsfixedgeneralmonotonicityarbitrarybendat--sherman
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We give new characterizations for matrix monotonicity and convexity of fixed order which connects previous characterizations by Loewner, Dobsch, Donoghue, Kraus and Bendat--Sherman. The ideas introduced are then used to characterize matrix monotone functions of arbitrary order on general subsets of the real line.
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