Description
Introductory Functional Analysis with Applications introduces the central concepts of functional analysis and their applications to problems in mathematics and the natural sciences. It develops the theory of metric and normed spaces, Banach spaces, Hilbert spaces, linear operators, and linear functionals, followed by fundamental results such as the Hahn–Banach, uniform boundedness, open mapping, and closed graph theorems. The book also discusses fixed-point methods, approximation theory, spectral theory, and compact and unbounded operators. Applications to differential and integral equations, approximation problems, and quantum mechanics demonstrate how the abstract theory can be used in concrete mathematical and scientific settings.
