Book chapter
Appendix A: Some Basics of Functional Analysis
Dynamics with Inequalities, pp.307-326
Other Titles in Applied Mathematics, Society for Industrial and Applied Mathematics
01/01/2011
DOI: 10.1137/1.9781611970715.appa
Abstract
When talking about things like vector spaces, the important thing is not how the space is defined or how it is constructed; what is important is how it behaves. This allows us to apply ideas from one area of mathematics to another if the object of discussion behaves in the right way. So we use an abstract definition of what a vector space is, rather than say “a vector is a collection of real numbers
x
1
,
x
2
, etc., arranged like this:
x
=
[
x
1
,
x
2
,
…
,
x
n
]
.” Then we can treat collections of functions as vectors if that gives us insight into the functions.
Readers may wish to turn to texts on mathematical analysis and partial differential equations for discussion of these topics in greater depth, such as [94, 151, 155, 168, 217, 213]. Specialized topics are treated in monographs: for vector-valued measures, see [78, 80]; for Sobolev spaces, see [1, 262]. A short but excellent book on optimization and fixed point theorems is [106].
Details
- Title: Subtitle
- Appendix A: Some Basics of Functional Analysis
- Creators
- David E Stewart - University of Iowa
- Resource Type
- Book chapter
- Publication Details
- Dynamics with Inequalities, pp.307-326
- Series
- Other Titles in Applied Mathematics
- DOI
- 10.1137/1.9781611970715.appa
- Publisher
- Society for Industrial and Applied Mathematics
- Language
- English
- Date published
- 01/01/2011
- Academic Unit
- Mathematics
- Record Identifier
- 9984242341702771
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