Linear Functional Analysis PDF
by Bryan Rynne, M.A. Youngson
Part of the Springer Undergraduate Mathematics Series series
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This book provides an introduction to the ideas and methods of linear func- tional analysis at a level appropriate to the final year of an undergraduate course at a British university.
The prerequisites for reading it are a standard undergraduate knowledge of linear algebra and real analysis (including the the- ory of metric spaces).
Part of the development of functional analysis can be traced to attempts to find a suitable framework in which to discuss differential and integral equa- tions.
Often, the appropriate setting turned out to be a vector space of real or complex-valued functions defined on some set.
In general, such a vector space is infinite-dimensional.
This leads to difficulties in that, although many of the elementary properties of finite-dimensional vector spaces hold in infinite- dimensional vector spaces, many others do not.
For example, in general infinite- dimensional vector spaces there is no framework in which to make sense of an- alytic concepts such as convergence and continuity.
Nevertheless, on the spaces of most interest to us there is often a norm (which extends the idea of the length of a vector to a somewhat more abstract setting).
Since a norm on a vector space gives rise to a metric on the space, it is now possible to do analysis in the space.
As real or complex-valued functions are often called functionals, the term functional analysis came to be used for this topic.
We now briefly outline the contents of the book.
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- Format:PDF
- Publisher:Springer London
- Publication Date:14/03/2013
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- ISBN:9781447136552
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Information
-
Download Now
- Format:PDF
- Publisher:Springer London
- Publication Date:14/03/2013
- Category:
- ISBN:9781447136552