Functional analysis (Q2748500)

This book is based on courses given by the author and completed later with topics from function theory, topology and global analysis. Its contents is developed in six chapters written with growing degree of difficulty and oriented towards applications. NEWLINENEWLINEBriefly, the first two chapters are devoted to basic facts of functional analysis such as Banach and Hilbert spaces, Baire category theorem and Hahn-Banach theorem, but they also include Sturm-Liouville problems and elliptic boundary value problems and eigenvalues. Chapters 3 and 4 consider the general spectral theory of bounded and unbounded linear operators, the classical theory of Riesz-Schauder, Fredholm operators, a scope of index theory of Fredholm operators and different applications to Toeplitz and singular integral operators. Chapter 5 is devoted to the spectral theory of unbounded operators and its applications to ordinary differential operators. The last chapter studies partial differential and pseudo-differential operators. NEWLINENEWLINEThroughout the book, the author gives motivation for the topics and their historic development, completes the exposition of the sections with exercises and gives many references. In particular, a long list of references appears at the end of the book, together with a list of symbols and name and subject indexes. NEWLINENEWLINEThe reviewer considers this is an excellent advanced text in functional analysis and its applications.