The main goal of the paper is to obtain explicit integral representations of implicit functions whose existence is guaranteed by the implicit function theory. We derive the mentioned representation ...

Let α and β be bounded measurable functions on the unit circle 𝕋. Then the singular integral operator Sα,β is defined by Sα,βf = αP+f + βP–f, (f ∈ L2(𝕋)) where P+ is an analytic projection and P– is ...