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- W3194787857 abstract "By a radial set we understand a non-empty set (A subset mathbb{C} setminus {0}) such that for every point (zin A) the circle with centre at the origin and passing through (z) is included in (A). We show in a detailed manner that every continuous and injective function (F : A to mathbb{C} setminus {0}) can be represented by means of the natural exponential function (text{exp}) and a certain continuous function (varPhi : text{Ei}(A) to mathbb{C}), where (text{Ei}(A)) is the set of all (z in mathbb{C}) with the property (text{exp}(iz) in A). The representation is given by (F(text{exp}(iz)) = text{exp}(ivarPhi (z))) for (z in text{Ei}(A)). We also touch the problem of the injectivity of (varPhi)." @default.
- W3194787857 created "2021-08-30" @default.
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- W3194787857 date "2021-07-24" @default.
- W3194787857 modified "2023-10-16" @default.
- W3194787857 title "Exponential representations of injective continuous mappings in radial sets" @default.
- W3194787857 doi "https://doi.org/10.17951/a.2021.75.1.37-51" @default.
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