Elements of the Theory of Functions and Functional Analysis - Kolmogorov and Fomin

DSA ADS Course - 2021

Elements of the Theory of Functions and Functional Analysis - Kolmogorov and Fomin

Functional Analysis, Theory of Functions, Set Theory, Metric Spaces, Normed Linear Spaces, Linear Operator Equation, Fredholm's Theorems

First part is metric and normal spaces, set theory and mappings, principle of contraction mappings and its applications to the proof of existence theorems in the theory of differential and integral equations, continuous curves in metric spaces, normed linear spaces, weak sequential convergence of elements and linear functionals, adjoint operators, and linear operator equations.

Part Two focuses on an exposition of measure theory, the Lebesque interval and Hilbert Space. Both parts feature numerous exercises at the end of each section and include helpful lists of symbols, definitions, and theorems.