Fourier Series in Control Theory-[Book review; V. Komornik and P. Loreti]

This book addresses some of the following topics: observation, control, and stabilization; well-posedness in a Riesz basis setting; observation of strings; observation of beams; vector sum estimates; problems on spherical domains; multidimensional Ingham-type theorems; a general Ingham-type theorem; and problems with weakened gap condition. The book attempts to unify certain inequalities and variations offered by Ingham under the rubric of the so-called harmonic analysis method. The book gives a very clear exposition of the method of Ingham-type inequalities. Although this method is rather limited in its applicability to higher dimension problems, it does give very strong and often optimal results where it does apply.