Fourier Transform and Fourier Series -- Operator-valued Fourier multipliers and functional calculus -- Maximal Lp-Regularity -- Parameter-Elliptic Boundary Value Problems in Cylindrical Domains -- Periodic and Mixed Dirichlet-Neumann Boundary Conditions for the Laplacian -- Stokes Problem and Helmholtz Projection in Rectangular Cylinders.

Tobias Nau addresses initial boundary value problems in cylindrical space domains with the aid of modern techniques from functional analysis and operator theory. In particular, the author uses concepts from Fourier analysis of functions with values in Banach spaces and the operator-valued functional calculus of sectorial operators. He applies abstract results to concrete problems in cylindrical space domains such as the heat equation subject to numerous boundary conditions and equations arising from fluid dynamics.