Floquet Transform and Direct Integral Decomposition

In Chapter 3, the main notions and techniques of multi-dimensional Floquet theory are introduced: Bloch and Floquet functions and the Floquet transform. The latter is the analog for the periodic case of the Fourier transform. Direct integral decomposition is introduced and studied. Important for the whole theory, the analogs of Plancherel and Paley–Wiener theorems are established. Analogously with the constant-coefficient case, these are invaluable tools throughout the book.