Banach-Hilbert Spaces, Vector Measures and Group Representations

An elementary introduction to classical analysis on normed spaces, with special attention paid to fixed points, calculus, and ordinary differential equations. It contains a full treatment of vector measures on delta rings without assuming any scalar measure theory and hence should fit well into existing courses. The relation between group representations and almost periodic functions is presented. The mean values offer an infinite-dimensional analogue of measure theory on finite-dimensional Euclidean spaces. The work should be suitable for beginners who want to get through the basic material as soon as possible and then do their own research immediately.