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- Applied functional analysis.
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It emerged as a distinct field in the 20th century, when it was realized that diverse mathematical processes, from arithmetic to calculus procedures, exhibit very similar properties. A functional, like a function, is a relationship between objects, but the objects may be numbers, vectors, or functions. Groupings of such objects are called spaces. Differentiation is an example of a functional because it defines a relationship between a function and another function its derivative.
Integration is also a functional.
Functional Analysis and Applications | CIMPA
Functional analysis focuses on classes of functions, such as those that can be differentiated or integrated. Functional analysis. Info Print Cite. Submit Feedback. Thank you for your feedback.
See Article History. One reason for doing this organization is that one often only needs a Banach-version of such results. Another reason is that this approach seems more pedagogically sound; the statement of the results in their full generality may obscure its simplicity.
Exercises are meant to be an unintegrated part of the book. They can be skipped altogether, and the book should be fully read and understood. Some alternative proofs and additional results are relegated as exercises when their inclusion may disrupt the flow of the exposition. Knowledge of measure theory will not be needed except for Chapter 6, where we formulate the spectrum theorem in the language of measure theory. As for topology, knowledge of metric spaces suffices for Chapter 1 and Chapter 2.
The solid background in general topology is required for the ensuing chapters. From Wikibooks, open books for an open world.
Introduction to Functional Analysis
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- Functional Analysis.
- Duke University Press - Annals of Functional Analysis.
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- Category:Functional analysis.
- Category:Functional analysis - Wikipedia.