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 di mensional vibrating systems (like strings and beams) and heating processes. Distributed as well as boundary control is considered. In the case of vibrating systems trigonometric moment pro blems are to be investigated which is done on the basis of an abstract moment theory in Hilbert spaces. Equivalently alsothe theory of linear operator equations on Hilbert spa ces ( 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 to be dealt with which is done on the basis of an ab stract moment theory in Banach spaces. Time minimal control lability is also treated with the aid of the theory of line aroperator equations on Banach spaces. Some advanced knowledge in functional analyis and on partial differential equations is preassumed for a fluent reader of the book but parts of it are also readable with basic ma thematical knowledge (for instance the finite dimensional part of the introduction)