Linear functional analysis

Bryan P. Rynne and Martin A. Youngson

This introduction to the ideas and methods of linear functional analysis shows how familiar and useful concepts from finite-dimensional linear algebra can be extended or generalized to infinite-dimensional spaces. Aimed at advanced undergraduates in mathematics and physics, the book assumes a standard background of linear algebra, real analysis (including the theory of metric spaces), and Lebesgue integration, although an introductory chapter summarizes the requisite material. A highlight of the second edition is a new chapter on the Hahn-Banach theorem and its applications to the theory of duality.

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[目次]

  • Preliminaries.- Normed Spaces.- Inner Product Spaces, Hilbert Spaces.- Linear Operators.- Duality and the Hahn-Banach Theorem.- Linear Operators on Hilbert Spaces.- Compact Operators.- Integral and Differential Equations.- Solutions to Exercises.

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この本の情報

書名 Linear functional analysis
著作者等 Rynne, Bryan P.
Rynne Bryan P. (Department of Mathematics Heriot-Watt University Edinburgh)
Youngson Martin A.
Youngson Martin Alexander
シリーズ名 Springer undergraduate mathematics series
出版元 Springer
刊行年月 c2008
版表示 2nd ed
ページ数 x, 324 p.
大きさ 24 cm
ISBN 9781848000049
NCID BA84486587
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言語 英語
出版国 イギリス
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