On Moment Theory and Controllability of One-Dimensional Vibrating Systems and Heating Processes

The main concern of this book is the application of infinite moment theory to the problem of controllability of one-dimensional vibrating systems (like strings and beams) and heating processes. Distributed control and boundary control are considered. In the case of vibrating systems, trigonometric moment problems are investigated on the basis of abstract moment theory in Hilbert spaces. Additionally, the theory of linear operator equations on Hilbert spaces (partly with unbounded operators) is applied to the problem of controllability and time-minimal controllability. In the case of heating processes, exponential moment problems are dealt with on the basis of abstract moment theory in Banach spaces. Time-minimal controllability is also treated with the aid of the theory of linear operator equations on Banach spaces. Some advanced knowledge in functional analysis and on partial differential equations is required for a full reading of the book, but parts of it are also readable with basic mathematical knowledge.