Complex Analysis of Real Functions I: Complex-Analytic Structure and\n Integrable Real Functions

A complex-analytic structure within the unit disk of the complex plane is\npresented. It can be used to represent and analyze a large class of real\nfunctions. It is shown that any integrable real function can be obtained by\nmeans of the restriction of an analytic function to the unit circle, including\nfunctions which are non-differentiable, discontinuous or unbounded. An explicit\nconstruction of the analytic functions from the corresponding real functions is\ngiven. The complex-analytic structure can be understood as an universal\nregulator for analytic operations on real functions.\n