Functional Analysis

Functional Analysis provides the framework, and a great deal of machinery, for much of modern mathematics: not only for pure mathematics (such as harmonic analysis and complex analysis) but also for the applications of mathematics, such as probability theory, the ordinary and partial differential equations met in applied mathematics, and the mathematical formulation of quantum mechanics.

The basic idea of Functional Analysis is to represent functions as points in an infinite-dimensional vector space. Since the space is infinite-dimensional, algebraic arguments are not enough, and it is necessary and appropriate to introduce the idea of convergence by a norm, which in turn defines a metric on the space.

Functional Analysis

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