000			04845nam a22005175i 4500
001			978-0-8176-4448-2
003			DE-He213
005			20251006084434.0
007			cr nn 008mamaa
008			121116s2005 xxu| s |||| 0|eng d
020			_a9780817644482
020			_a99780817644482
024	7		_a10.1007/978-0-8176-4448-2 _2doi
082	0	4	_a511.4 _223
100	1		_aChristensen, Ole. _eauthor.
245	1	0	_aApproximation Theory _h[electronic resource] : _bFrom Taylor Polynomials to Wavelets / _cby Ole Christensen, Khadija L. Christensen.
264		1	_aBoston, MA : _bBirkhäuser Boston : _bImprint: Birkhäuser, _c2005.
300			_aXI, 156 p. _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		_a1 Approximation with Polynomials -- 1.1 Approximation of a function on an interval -- 1.2 Weierstrass' theorem -- 1.3 Taylor's theorem -- 1.4 Exercises -- 2 Infinite Series -- 2.1 Infinite series of numbers -- 2.2 Estimating the sum of an infinite series -- 2.3 Geometric series -- 2.4 Power series -- 2.5 General infinite sums of functions -- 2.6 Uniform convergence -- 2.7 Signal transmission -- 2.8 Exercises -- 3 Fourier Analysis -- 3.1 Fourier series -- 3.2 Fourier's theorem and approximation -- 3.3 Fourier series and signal analysis -- 3.4 Fourier series and Hilbert spaces -- 3.5 Fourier series in complex form -- 3.6 Parseval's theorem -- 3.7 Regularity and decay of the Fourier coefficients -- 3.8 Best N-term approximation -- 3.9 The Fourier transform -- 3.10 Exercises -- 4 Wavelets and Applications -- 4.1 About wavelet systems -- 4.2 Wavelets and signal processing -- 4.3 Wavelets and fingerprints -- 4.4 Wavelet packets -- 4.5 Alternatives to wavelets: Gabor systems -- 4.6 Exercises -- 5 Wavelets and their Mathematical Properties -- 5.1 Wavelets and L2 (?) -- 5.2 Multiresolution analysis -- 5.3 The role of the Fourier transform -- 5.4 The Haar wavelet -- 5.5 The role of compact support -- 5.6 Wavelets and singularities -- 5.7 Best N-term approximation -- 5.8 Frames -- 5.9 Gabor systems -- 5.10 Exercises -- Appendix A -- A.1 Definitions and notation -- A.2 Proof of Weierstrass' theorem -- A.3 Proof of Taylor's theorem -- A.4 Infinite series -- A.5 Proof of Theorem 3 7 2 -- Appendix B -- B.1 Power series -- B.2 Fourier series for 2?-periodic functions -- List of Symbols -- References.
520			_aThis concisely written book gives an elementary introduction to a classical area of mathematics-approximation theory-in a way that naturally leads to the modern field of wavelets. The exposition, driven by ideas rather than technical details and proofs, demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications. Key features and topics: * Description of wavelets in words rather than mathematical symbols * Elementary introduction to approximation using polynomials (Weierstrass' and Taylor's theorems) * Introduction to infinite series, with emphasis on approximation-theoretic aspects * Introduction to Fourier analysis * Numerous classical, illustrative examples and constructions * Discussion of the role of wavelets in digital signal processing and data compression, such as the FBI's use of wavelets to store fingerprints * Minimal prerequisites: elementary calculus * Exercises that may be used in undergraduate and graduate courses on infinite series and Fourier series Approximation Theory: From Taylor Polynomials to Wavelets will be an excellent textbook or self-study reference for students and instructors in pure and applied mathematics, mathematical physics, and engineering. Readers will find motivation and background material pointing toward advanced literature and research topics in pure and applied harmonic analysis and related areas.
650		0	_aMATHEMATICS.
650		0	_aHARMONIC ANALYSIS.
650		0	_aFOURIER ANALYSIS.
650		0	_aFUNCTIONAL ANALYSIS.
650	1	4	_aMATHEMATICS.
650	2	4	_aAPPROXIMATIONS AND EXPANSIONS.
650	2	4	_aABSTRACT HARMONIC ANALYSIS.
650	2	4	_aFOURIER ANALYSIS.
650	2	4	_aFUNCTIONAL ANALYSIS.
650	2	4	_aAPPLICATIONS OF MATHEMATICS.
650	2	4	_aSIGNAL, IMAGE AND SPEECH PROCESSING.
700	1		_aChristensen, Khadija L. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817636005
830		0	_aApplied and Numerical Harmonic Analysis
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-4448-2 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c59644 _d59644