Linear & Functional Analysis, Bryan P. Rynne and Martin A. Youngson

Judul/Title: Linear Functional Analysis
Penulis/Author: Bryan P. Rynne and Martin A. Youngson
Penerbit/Publisher: Springer
Edisi/Edition: 2008
Halaman/Pages: 324
Dimensi/Dimension: 17 x 24 x 2cm
Sampul/Cover: Hardcover & Hardcopy
Bahasa/Language: English
Harga/Price: Rp. 125.000,-
Call No.:
Status: Ada/Available

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This book provides an introduction to the ideas and methods of linear functional analysis at a level appropriate to the final year of an undergraduate course at British university. The prerequisites for reading it are a standard undergraduate knowledge of linear algebra and real analysis (including the theory 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 equations. 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 not. For examples, in general infinite-dimensional vector spaces there is no framework in which to make sense of analytic concepts such as convergence and continuity. Nevertheless, on the spaces of most interest to us there is often to 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 functional, the term functional analysis same to be used for this topic.