The unifying approach of functional analysis is to view functions as points in some abstract vector space and the differential and integral operators as linear transformations on these spaces. It has been the author's goal to present the basics of functional analysis in a way that makes them comprehensible to a student who has completed first courses in linear algebra and real analysis, and to develop the topics in their historical context.

Inhalt

• Metric Spaces, Normed Spaces, Inner Product Spaces The Topology of Metric Spaces Measure and Integration Fourier Analysis in Hilbert Space An Introduction to Abstract Linear Operator Theory Further Topics Appendix A: Complex Numbers * Appendix B: Basic Set Theory