វិភាគអនុគមន៍

Functional Analysis

Asst. Prof: Chum Veasna

Functional Analysis

Functional Analysis is founded on a geometric approach to the study of objects that are actually analytic in nature: functions, equations, series, sequences. This approach, which enables one to use geometric intuition in complicated analytic problems, proved to be highly productive.

Powerful methods were developed in the framework of Functional Analysis that found application in a variety of fields of mathematics. The language of Functional Analysis found its way into branches of pure and applied mathematics such as Harmonic Analysis, Differential and Integral Equations, Approximate Computation Methods, Linear Programming, Optimization Methods, and this list of applications could go on.

Functional analysis is the study of functions and operators, a kind of higher-level version of basic real analysis. In most, if not all, research areas of applied mathematics, you will be faced with having to perform “operations" that require solid mathematical justification, even if they always appear to work, for example, numerically, since there should always be a mathematical basis for why they work, or, indeed, when they are expected to work and not to work.

The present textbook is also an attempt to represent the main ideas and directions of such applications, first and foremost to questions in Harmonic Analysis.