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- W2949948373 abstract "In classical complex analysis analyticity of a complex function f is equivalent to differentiability of its real and imaginary parts u and v, respectively, together with the Cauchy-Riemann equations for the partial derivatives of u and v. We extend this result to the context of free noncommutative functions in operator systems. In this context, the real and imaginary parts become so called real noncommutative functions, as appeared recently in the context of Lowner’s theorem in several noncommutative variables. Additionally, as part of our investigation of real noncommutative functions, we show that real noncommutative functions are in fact noncommutative functions." @default.
- W2949948373 created "2019-06-27" @default.
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- W2949948373 date "2020-01-01" @default.
- W2949948373 modified "2023-09-27" @default.
- W2949948373 title "Cauchy-Riemann Equations for Free Noncommutative Functions" @default.
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- W2949948373 doi "https://doi.org/10.1007/978-3-030-43380-2_15" @default.
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