An introduction to wavelets through linear algebra. Undergraduate texts in mathematics

Frazier, Michael W.:

ISBN 10: 0387986391 / ISBN 13: 9780387986395

Editore: New York ; Berlin ; Heidelberg ; Barcelona ; Hong Kong ; London ; Milan ; Paris ; Singapore ; Tokyo : Springer, 1999

Riguardo questo articolo

XVI, 501 Seiten ; 25 cm SEHR schönes Exemplar der ERSTAUSGABE. IN VERY good shape. ( We offer a lot of books on PHYSICS and MATHEMATICS on stock in EXCELLENT shape). Sprache: Französisch Gewicht in Gramm: 890.

Codice articolo 297808

Dati bibliografici

• Titolo: An introduction to wavelets through linear algebra. Undergraduate texts in mathematics
• Editore: New York ; Berlin ; Heidelberg ; Barcelona ; Hong Kong ; London ; Milan ; Paris ; Singapore ; Tokyo : Springer
• Data di pubblicazione: 1999
• Lingua: Francese
• ISBN 10: 0387986391
• ISBN 13: 9780387986395
• Rilegatura: Originalpappband.
• Edizione: First edition.
• Condizione: Wie neu
• Cataloghi dei venditori:
  • Mathematik

Descrizione articolo

Riassunto

Wavelet theory is on the boundary between mathematics and engineering, making it ideal for demonstrating to students that mathematics research is thriving in the modern day. Students can see non-trivial mathematics ideas leading to natural and important applications, such as video compression and the numerical solution of differential equations. The only prerequisites assumed are a basic linear algebra background and a bit of analysis background. Intended to be as elementary an introduction to wavelet theory as possible, the text does not claim to be a thorough or authoritative reference on wavelet theory.

Contenuti

Preface Acknowledgments Prologue: Compression of the FBI Fingerprint Files 1 Background: Complex Numbers and Linear Algebra 1.1 Real Numbers and Complex Numbers 1.2 Complex Series, Euler's Formula, and the Roots of Unity 1.3 Vector Spaces and Bases 1.4 Linear Transformations, Matrices, and Change of Basis 1.5 Diagonalization of Linear Transformations and Matrices 1.6 Inner Products, Orthonormal Bases, and Unitary Matrices 2 The Discrete Fourier Transform 2.1 Basic Properties of the Discrete Fourier Transform 2.2 Translation-Invariant Linear Transformations 2.3 The Fast Fourier Transform 3 Wavelets on $bZ_N$ 3.1 Construction of Wavelets on $bZ_N$: The First Stage 3.2 Construction of Wavelets on $bZ_N$: The Iteration Step 3.3 Examples and Applications 4 Wavelets on $bZ$ 4.1 $\ell ^2(bZ)$ 4.2 Complete Orthonormal Sets in Hilbert Spaces 4.3 $L^2([-\pi ,\pi ))$ and Fourier Series 4.4 The Fourier Transform and Convolution on $\ell ^2(bZ)$ 4.5 First-Stage Wavelets on $bZ$ 4.6 The Iteration Step for Wavelets on $bZ$ 4.7 Implementation and Examples 5 Wavelets on $bR$ 5.1 $L^2(bR)$ and Approximate Identities 5.2 The Fourier Transform on $bR$ 5.3 Multiresolution Analysis and Wavelets 5.4 Construction of Multiresolution Analyses 5.5 Wavelets with Compact Support and Their Computation 6 Wavelets and Differential Equations 6.1 The Condition Number of a Matrix 6.2 Finite Difference Methods for Differential Equations 6.3 Wavelet-Galerkin Methods for Differential Equations Bibliography Index