This book gives an introduction to Linear Functional Analysis, which is a synthesis of algebra, topology, and analysis. In addition to the basic theory it explains operator theory, distributions, Sobolev spaces, and many other things. The text is self-contained and includes all proofs, as well as many exercises, most of them with solutions. Moreover, there are a number of appendices, for example on Lebesgue integration theory. A complete introduction to the subject, Linear Functional Analysis will be particularly useful to readers who want to quickly get to the key statements and who are interested in applications to differential equations.
Professor Alt's work has had a significant impact on the areas of applied analysis and partial differential equations, in particular in the applications to mechanics and thermodynamics. Recently, he worked in the mathematical theory of phase transition and made contributions to the entropy principle. Alt was professor at the Institute of Applied Mathematics at the University of Bonn, and since 2011 lectures as Honorary Professor at the Technical University of Munich.
Introduction.- Preliminaries.- Function spaces.- Subsets of function spaces.- Linear operators.- Linear functionals.- Uniform boundedness principle.- Weak convergence.- Finite-dimensional approximation.- Compact operators.- Spectrum of compact operators.- Self-adjoint operators.- References.- Symbols.- Index.