000			04041nam a22005415i 4500
001			978-0-8176-4980-7
003			DE-He213
005			20251006084440.0
007			cr nn 008mamaa
008			100528s2010 xxu| s |||| 0|eng d
020			_a9780817649807
020			_a99780817649807
024	7		_a10.1007/978-0-8176-4980-7 _2doi
082	0	4	_a515.7 _223
100	1		_aChristensen, Ole. _eauthor.
245	1	0	_aFunctions, Spaces, and Expansions _h[electronic resource] : _bMathematical Tools in Physics and Engineering / _cby Ole Christensen.
264		1	_aBoston : _bBirkhäuser Boston, _c2010.
300			_aXIX, 266 p. 9 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aApplied and Numerical Harmonic Analysis
505	0		_aMathematical Background -- Normed Vector Spaces -- Banach Spaces -- Hilbert Spaces -- The Lp-spaces -- The Hilbert Space L2 -- The Fourier Transform -- An Introduction to Wavelet Analysis -- A Closer Look at Multiresolution Analysis -- B-splines -- Special Functions -- Appendix A -- Appendix B.
520			_aThis graduate-level textbook is a detailed exposition of key mathematical tools in analysis aimed at students, researchers, and practitioners across science and engineering. Every topic covered has been specifically chosen because it plays a key role outside the field of pure mathematics. Although the treatment of each topic is mathematical in nature, and concrete applications are not delineated, the principles and tools presented are fundamental to exploring the computational aspects of physics and engineering. A central theme of the book is the structure of various vector spaces-most importantly, Hilbert spaces-and expansions of elements in these spaces in terms of bases. Key topics and features include: * More than 150 exercises * Abstract and normed vector spaces * Approximation in normed vector spaces * Hilbert and Banach spaces * General bases and orthonormal bases * Linear operators on various normed spaces * The Fourier transform, including the discrete Fourier transform * Wavelets and multiresolution analysis * B-splines * Sturm-Liouville problems As a textbook that provides a deep understanding of central issues in mathematical analysis, Functions, Spaces, and Expansions is intended for graduate students, researchers, and practitioners in applied mathematics, physics, and engineering. Readers are expected to have a solid understanding of linear algebra, in Rn and in general vector spaces. Familiarity with the basic concepts of calculus and real analysis, including Riemann integrals and infinite series of real or complex numbers, is also required. Functions, Spaces, and Expansions is the main textbook for the e-course Mathematics 4: Real Analysis currently being taught at the Technical University of Denmark. Please click the "Course Materials" link on the right to access videos of the lectures, problem sheets, and solutions to selected exercises.
650		0	_aMATHEMATICS.
650		0	_aFOURIER ANALYSIS.
650		0	_aFUNCTIONAL ANALYSIS.
650		0	_aFUNCTIONS, SPECIAL.
650		0	_aCOMPUTER SCIENCE.
650		0	_aMATHEMATICAL PHYSICS.
650		0	_aENGINEERING MATHEMATICS.
650	1	4	_aMATHEMATICS.
650	2	4	_aFUNCTIONAL ANALYSIS.
650	2	4	_aAPPL.MATHEMATICS/COMPUTATIONAL METHODS OF ENGINEERING.
650	2	4	_aMATHEMATICAL METHODS IN PHYSICS.
650	2	4	_aSPECIAL FUNCTIONS.
650	2	4	_aFOURIER ANALYSIS.
650	2	4	_aCOMPUTATIONAL SCIENCE AND ENGINEERING.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817649791
830		0	_aApplied and Numerical Harmonic Analysis
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-4980-7 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c59837 _d59837