Solutions to Penrose's ‘Road To Reality’
Chapter 9: Fourier decomposition and hyperfunctions

§9.1 Fourier series
9.1 * Fourier decomposition in terms of the complex exponential
9.2 ** Coefficients of the Lauent series
§9.3 Frequency splitting on the Riemann sphere
9.3 ** Splitting of analytic functions along the unit circle
9.4 ** Biholomorphisms of the unit disc
9.5 ** Mapping the unit circle to the real line
§9.4 The Fourier transform
9.6 *** Fourier integral theorem
§9.5 Frequency splitting from the Fourier transform
9.7 * A circle in the complex plane
§9.6 What kind of function is appropriate?
9.8 * The square-wave function (I): The Laurent series
9.9 ** The square-wave function (II): Two partial sums of the Laurent series
9.10 * The square-wave function (III): Adding the partial sums
9.11 ** The square-wave function (IV): Reconstructing the square-wave
§9.7 Hyperfunctions
9.12 * Two ways to define a hyperfunction
9.13 ** Multiplying a hyperfunction with a function
9.14 ** The Dirac delta function as a hyperfunction