000			04695nam a22005175i 4500
001			978-0-8176-4687-5
003			DE-He213
005			20251006084438.0
007			cr nn 008mamaa
008			101109s2011 xxu| s |||| 0|eng d
020			_a9780817646875
020			_a99780817646875
024	7		_a10.1007/978-0-8176-4687-5 _2doi
082	0	4	_a515.785 _223
100	1		_aHeil, Christopher. _eauthor.
245	1	2	_aA Basis Theory Primer _h[electronic resource] : _bExpanded Edition / _cby Christopher Heil.
264		1	_aBoston : _bBirkhäuser Boston, _c2011.
300			_aXXV, 537p. 42 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		_aANHA Series Preface -- Preface -- General Notation -- Part I. A Primer on Functional Analysis -- Banach Spaces and Operator Theory -- Functional Analysis -- Part II. Bases and Frames -- Unconditional Convergence of Series in Banach and Hilbert Spaces -- Bases in Banach Spaces -- Biorthogonality, Minimality, and More About Bases -- Unconditional Bases in Banach Spaces -- Bessel Sequences and Bases in Hilbert Spaces -- Frames in Hilbert Spaces -- Part III. Bases and Frames in Applied Harmonic Analysis -- The Fourier Transform on the Real Line -- Sampling, Weighted Exponentials, and Translations -- Gabor Bases and Frames -- Wavelet Bases and Frames -- Part IV. Fourier Series -- Fourier Series -- Basic Properties of Fourier Series -- Part V. Appendices -- Lebesgue Measure and Integration -- Compact and Hilbert-Schmidt Operators -- Hints for Exercises -- Index of Symbols -- References -- Index.
520			_aThe classical subject of bases in Banach spaces has taken on a new life in the modern development of applied harmonic analysis. This textbook is a self-contained introduction to the abstract theory of bases and redundant frame expansions and its use in both applied and classical harmonic analysis. The four parts of the text take the reader from classical functional analysis and basis theory to modern time-frequency and wavelet theory. * Part I develops the functional analysis that underlies most of the concepts presented in the later parts of the text. * Part II presents the abstract theory of bases and frames in Banach and Hilbert spaces, including the classical topics of convergence, Schauder bases, biorthogonal systems, and unconditional bases, followed by the more recent topics of Riesz bases and frames in Hilbert spaces. * Part III relates bases and frames to applied harmonic analysis, including sampling theory, Gabor analysis, and wavelet theory. * Part IV deals with classical harmonic analysis and Fourier series, emphasizing the role played by bases, which is a different viewpoint from that taken in most discussions of Fourier series. Key features: * Self-contained presentation with clear proofs accessible to graduate students, pure and applied mathematicians, and engineers interested in the mathematical underpinnings of applications. * Extensive exercises complement the text and provide opportunities for learning-by-doing, making the text suitable for graduate-level courses; hints for selected exercises are included at the end of the book. * A separate solutions manual is available for instructors upon request at: www.birkhauser-science.com/978-0-8176-4686-8/. * No other text develops the ties between classical basis theory and its modern uses in applied harmonic analysis. A Basis Theory Primer is suitable for independent study or as the basis for a graduate-level course. Instructors have several options for building a course around the text depending on the level and background of their students.
650		0	_aMATHEMATICS.
650		0	_aHARMONIC ANALYSIS.
650		0	_aFOURIER ANALYSIS.
650		0	_aFUNCTIONAL ANALYSIS.
650		0	_aENGINEERING MATHEMATICS.
650	1	4	_aMATHEMATICS.
650	2	4	_aABSTRACT HARMONIC ANALYSIS.
650	2	4	_aAPPL.MATHEMATICS/COMPUTATIONAL METHODS OF ENGINEERING.
650	2	4	_aFUNCTIONAL ANALYSIS.
650	2	4	_aFOURIER ANALYSIS.
650	2	4	_aAPPLICATIONS OF MATHEMATICS.
650	2	4	_aSIGNAL, IMAGE AND SPEECH PROCESSING.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817646868
830		0	_aApplied and Numerical Harmonic Analysis
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-4687-5 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c59759 _d59759