Abstract:We adapt the "royal road" method used to simplify automatic analyticity theorems in noncommutative function theory to several complex variables. We show that certain families of functions must be real analytic if they have certain nice properties on one dimensional slices.) is a matrix monotone function of t whenever t ∈ (0, 1), the ϕ i are automorphisms of the upper half plane, and the tuple (ϕ 1 (t), . . . , ϕ d (t)) maps (0, 1) into E. We use the "royal road" to show that a function is matrix monotone lite … Show more
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