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˜The œillustrated wavelet transform handbook / par Addison,, Napler. Publication : [S.l.] : Taylor & Francis, 2002 . 400 p. ; , Contents Preface Chapter 1: Getting started Chapter 2: The continuous wavelet transform 2.1 Introduction 2.2 The Wavelet 2.3 Requirements for the Wavelet 2.4 The Energy Spectrum of the Wavelet 2.5 The Wavelet Transform 2.6 Identification of Coherent Structures 2.7 Edge Detection 2.8 The Inverse Wavelet Transform 2.9 The Signal Energy: Wavelet Based Energy and Power Spectra 2.10 The Wavelet Transform in Terms of the Fourier Transform 2.11 Complex Wavelets: The Morlet Wavelet 2.12 The Wavelet Transform, Short Time Fourier Transform and Heisenberg Boxes 2.13 Adaptive Transforms: Matching Pursuits 2.14 Wavelets in Two or More Dimensions 2.15 The CWT: Computation, Boundary Effects and Viewing 2.16 Endnotes 2.16.1 Chapter Key Words and Phrases 2.16.2 Further Resources Chapter 3: The Discrete Wavelet Transform 3.1 Introduction 3.2 Frames and Orthogonal Wavelet Bases 3.2.1 Frames 3.2.2 Dyadic Grid Scaling and Orthonormal Wavelet Transforms 3.2.3 The Scaling Function and the Multiresolution Representation 3.2.4 The Scaling Equation, Scaling Coefficients and Associated Wavelet Equation 3.2.5 The Haar Wavelet 3.2.6 Coefficients from Coefficients: The Fast Wavelet Transform 3.3 Discrete Input Signals of Finite Length 3.3.1 Approximations and Details 3.3.2 The Multiresolution Algorithm - An Example 3.3.3 Wavelet Energy 3.3.4 Alternative Indexing of Dyadic Grid Coefficients 3.3.5 A Simple Worked Example: The Haar Wavelet Transform 3.4 Everything Discrete 3.4.1 Discrete Experimental Input Signals 3.4.2 Smoothing, Thresholding and Denoising 3.5 Daubechies Wavelets 3.5.1 Filtering 3.5.2 Symmlets and Coiflets 3.6 Translation Invariance 3.7 Biorthogonal Wavelets 3.8 Two-Dimensional Wavelet Transforms 3.9 Adaptive Transforms: Wavelet Packets 3.10 Endnotes 3.10.1 Chapter Key Words and Phrases 3.10.2 Further Resources CHAPTER 4: FLUIDS 4.1 Introduction 4.2 Statistical Measures 4.2.1 Moments, Energy and Power Spectra 4.2.2 Intermittency and Correlation 4.2.3 Wavelet Thresholding 4.2.4 Wavelet Selection using Entropy Measures 4.3 Engineering Flows 4.3.1 Jets, Wakes, Turbulence and Coherent Structures 4.3.2 Fluid-Structure Interaction 4.3.3 Two-Dimensional Flow Fields 4.4 Geophysical Flows 4.4.1 Atmospheric Processes 4.4.2 Ocean Processes 4.5 Other Applications in Fluids and Further Resources CHAPTER 5: ENGINEERING TESTING, MONITORING AND CHARACTERISATION 5.1 Introduction 5.2 Machining Processes: Control, Chatter, Wear and Breakage 5.3 Rotating Machinery 5.3.1 Gears 5.3.2 Shafts, Bearings and Blades 5.4 Dynamics 5.5 Chaos 5.6 Non-Destructive Testing 5.7 Surface Characterisation 5.8 Other Applications in Engineering and Further Resources 5.8.1 Impacting 5.8.2 Data Compression 5.8.3 Engines 5.8.4 Miscellaneous CHAPTER 6: MEDICINE 6.1 Introduction 6.2 The Electrocardiogram 6.2.1 ECG Timing, Distortions and Noise 6.2.2 Detection of Abnormalities 6.2.3 Heart Rate Variability 6.2.4 Cardiac Arrhythmias 6.2.5 ECG Data Compression 6.3 Neuroelectric Waveforms 6.3.1 Evoked Potentials and Event-Related Potentials 6.3.2 Epileptic Seizures and Epileptogenic Foci 6.3.3 Classification of the EEG using Artificial Neural Networks 6.4 Pathological Sounds, Ultrasounds and Vibrations 6.4.1 Blood Flow Sounds 6.4.2 Heart Sounds and Heart Rates 6.4.3 Lung Sounds 6.4.4 Acoustic Response 6.5 Blood Flow and Blood Pressure 6.6 Medical Imaging 6.6.1 Ultrasonic Images 6.6.2 Magnetic Resonance Imaging, Computed Tomography and other Radiographic Images 6.6.3 Optical Imaging 6.7 Other Applications in Medicine 6.7.1 Electromyographic Signals 6.7.2 Sleep Apnea 6.7.3 DNA 6.7.4 Miscellaneous 6.7.5 Further Resources CHAPTER 7: FRACTALS, FINANCE, GEOPHYSICS AND OTHER AREAS 7.1 Introduction 7.2 Fractals 7.2.1 Exactly Self-Similar Fractals 7.2.2 Stochastic Fractals 7.2.3 Multifractals 7.3 Finance 7.4 Geophysics 7.4.1 Properties of Subsurface Media 7.4.2 Surface Fea. 26 cm. Date : 2002 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

A Course of modern analysis / par Whittaker, E.T. Publication : [S.l.] : Cambridge University Press, 1996 . 616 p. ; , This classic text has entered and held the field as the standard book on the applications of analysis to the transcendental functions. The authors explain the methods of modern analysis in the first part of the book and then proceed to a detailed discussion of the transcendental function, unhampered by the necessity of continually proving new theorems for special applications. In this way the authors have succeeded in being rigorous without imposing on the reader the mass of detail that so often tends to make a rigorous demonstration tedious. Researchers and students will find this book as valuable as ever. 23 cm. Date : 1996 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

A first course in harmonic analysis par Deitmar, Anton. Publication : [S.l.] Springer 2010 . 192 p. , Affordable softcover second edition of bestselling title (over 1000 copies sold of previous edition) A primer in harmonic analysis on the undergraduate level Gives a lean and streamlined introduction to the central concepts of this beautiful and utile theory. Entirely based on the Riemann integral and metric spaces instead of the more demanding Lebesgue integral and abstract topology. Almost all proofs are given in full and all central concepts are presented clearly. Provides an introduction to Fourier analysis, leading up to the Poisson Summation Formula. Make the reader aware of the fact that both principal incarnations of Fourier theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups. Introduces the reader to the techniques used in harmonic analysis of noncommutative groups. These techniques are explained in the context of matrix groups as a principal example. 24 cm. Date : 2010 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Abelian harmonic analysis, theta functions, and function algebra on a nilmanifold par Auslander, Louis. Publication : Berlin | New York Springer-Verlag 1975 . 1 online resource (98 pages). , Electronic reproduction.. [S.l.] :, 2010. Date : 1975 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Abstract harmonic analysis of continuous wavelet transforms / par Fuehr,, Hartmut. Publication : New York : Springer, 2005 . x, 193 p. ; 24 cm. Date : 2005 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

An Introduction to harmonic analysis on semisimple lie groups / par Varadarajan, V.S. Publication : [S.l.] : Cambridge University Press, 1999 . 326 p. ; , Broché. 23 cm. Date : 1999 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Analyse harmonique dans les systemes de tits bornologique de type affine par Matsumoto, H. Publication : [S.l.] Springer 1977 . 219 p. 24 cm. Date : 1977 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Commutative harmonic analysis par Khavin, V. P. Publication : Berlin Springer 1991 . 268 p. , This is the first volume in the subseries Commutative Harmonic Analysis of the EMS. It is intended for anyone who wants to get acquainted with the discipline. The first article is a large introduction, also serving as a guide to the rest of the volume. Starting from Fourier analysis of periodic function, then going through the Fourier transform and distributions, the exposition leads the reader to the group theoretic point of view. Numer- rous examples illustrate the connections to differential and integral equations, approximation theory, number theory, probability theory and physics. The article also contains a brief historical essay on the development of Fourier analysis. The second article focuses on some of the classical problems of Fourier series; it's a "mini-Zygmund" for the beginner. In particular, the convergence and summability of Fourier series, translation invariant operators and theorems on Fourier coefficients are given special attention. The third article is the most modern of the three, concentrating on the theory of singular integral operators. The simplest such operator, the Hilbert transform, is covered in detail. There is also a thorough introduction to Calderon-Zygmund theory. 24 cm. Date : 1991 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (2), La bibliothèque des Sciences Exactes et Naturelles (1),

Harmonic analysis / par Stein, Elias M. Publication : [S.l.] : Princeton University Press, 1993 . 716 p. ; , This book contains an exposition of some of the main developments of the last twenty years in the following areas of harmonic analysis: singular integral and pseudo-differential operators, the theory of Hardy spaces, Lsup estimates involving oscillatory integrals and Fourier integral operators, relations of curvature to maximal inequalities, and connections with analysis on the Heisenberg group. 24 cm. Date : 1993 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Harmonic analysis in phase space. / par Folland, Gerald B. Publication : [S.l.] : Princeton University Press, 1989 . 288 p. ; , This book provides the first coherent account of the area of analysis that involves the Heisenberg group, quantization, the Weyl calculus, the metaplectic representation, wave packets, and related concepts. This circle of ideas comes principally from mathematical physics, partial differential equations, and Fourier analysis, and it illuminates all these subjects. The principal features of the book are as follows: a thorough treatment of the representations of the Heisenberg group, their associated integral transforms, and the metaplectic representation; an exposition of the Weyl calculus of pseudodifferential operators, with emphasis on ideas coming from harmonic analysis and physics; a discussion of wave packet transforms and their applications; and a new development of Howe's theory of the oscillator semigroup. 23 cm. Date : 1989 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Harmonic analysis, group representations, automorphic forms and invariant theory : in honor of roger E. howe par Li, Jian-shu. Publication : [S.l.] World Scientific Publishing Company 2007 . 429 p. , This volume carries the same title as that of an international conference held at the National University of Singapore, 9 11 January 2006 on the occasion of Roger E. Howe s 60th birthday. Authored by leading members of the Lie theory community, these contributions, expanded from invited lectures given at the conference, are a fitting tribute to the originality, depth and influence of Howe s mathematical work. The range and diversity of the topics will appeal to a broad audience of research mathematicians and graduate students interested in symmetry and its profound applications. 23 cm. Date : 2007 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

A Panorama of harmonic analysis / par Krantz, Steven G. Publication : . 1 online resource (xvi, 357 pages) : Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Causal symmetric spaces : geometry and harmonic analysis / par Hilgert, Joachim. Publication : . 1 online resource (xiv, 286 pages) Disponibilité :  http://www.sciencedirect.com/science/book/9780125254304,

Unitary representations and harmonic analysis : an introduction / par Sugiura, Mitsuo, Publication : . 1 online resource (xv, 452 pages) Disponibilité :  http://www.sciencedirect.com/science/book/9780444885937,  http://www.sciencedirect.com/science/publication?issn=09246509&volume=44,

Groupoid Metrization Theory With Applications to Analysis on Quasi-Metric Spaces and Functional Analysis / par Mitrea, Dorina. Publication : . XII, 479 p. 1 illus. Disponibilité :  http://dx.doi.org/10.1007/978-0-8176-8397-9,

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