000			03800nam a22005295i 4500
001			978-1-84800-005-6
003			DE-He213
005			20161121231212.0
007			cr nn 008mamaa
008			100301s2008 xxk| s |||| 0|eng d
020			_a9781848000056 _9978-1-84800-005-6
024	7		_a10.1007/978-1-84800-005-6 _2doi
050		4	_aQA319-329.9
072		7	_aPBKF _2bicssc
072		7	_aMAT037000 _2bisacsh
082	0	4	_a515.7 _223
100	1		_aRynne, Bryan P. _eauthor.
245	1	0	_aLinear Functional Analysis _h[electronic resource] / _cby Bryan P. Rynne, Martin A. Youngson.
264		1	_aLondon : _bSpringer London, _c2008.
300			_aX, 324 p. 6 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aSpringer Undergraduate Mathematics Series, _x1615-2085
505	0		_aPreliminaries -- 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.
520			_aThis 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. The initial chapters develop the theory of infinite-dimensional normed spaces, in particular Hilbert spaces, after which the emphasis shifts to studying operators between such spaces. Functional analysis has applications to a vast range of areas of mathematics; the final chapters discuss the particularly important areas of integral and differential equations. Further highlights of the second edition include: a new chapter on the Hahn–Banach theorem and its applications to the theory of duality. This chapter also introduces the basic properties of projection operators on Banach spaces, and weak convergence of sequences in Banach spaces - topics that have applications to both linear and nonlinear functional analysis; extended coverage of the uniform boundedness theorem; plenty of exercises, with solutions provided at the back of the book. Praise for the first edition: "The authors write with a strong narrative thrust and a sensitive appreciation of the needs of the average student so that, by the final chapter, there is a real feeling of having 'gotten somewhere worth getting' by a sensibly paced, clearly signposted route." Mathematical Gazette "It is a fine book, with material well-organized and well-presented. A particularly useful feature is the material on compact operators and applications to differential equations." CHOICE.
650		0	_aMathematics.
650		0	_aMathematical analysis.
650		0	_aAnalysis (Mathematics).
650		0	_aFunctional analysis.
650		0	_aOperator theory.
650		0	_aPhysics.
650	1	4	_aMathematics.
650	2	4	_aFunctional Analysis.
650	2	4	_aOperator Theory.
650	2	4	_aAnalysis.
650	2	4	_aMathematical Methods in Physics.
700	1		_aYoungson, Martin A. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781848000049
830		0	_aSpringer Undergraduate Mathematics Series, _x1615-2085
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-84800-005-6
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c510061 _d510061