Notes: | This interesting textbook, in its first eight chapters, presents a very clear and elegant exposition of the basic notions of the theory of Hilbert space. Chapters 9 to 11 describe applications to Sturm-Liouville systems, Green functions and eigenfunction expansions. Of special interest is the material and treatment in Chapters 12–16: It is beautiful and relatively recent mathematics, dealing with positive operators, contractions, Hardy spaces, Hankel operators, applications to complex analysis and engineering, and the theorems of Parrot, Nehari, Kronecker and Adamyan-Arov-Kreĭn. The first half of the book is accessible to undergraduate students, and the second half may be used for graduate courses and would also be of interest to some electrical engineers. (MSN) |