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˜The œevolution of applied harmonic analysis / par Prestini,, Elena, Publication : Boston : Birkhauser, 2004 . xix, 349 p. : , Rev. ed. of: Applicazioni dell'analisi armonica. Milan : Ulrico Hoepli, 1996. 24 cm. Date : 2004 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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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),

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A course in abstract harmonic analysis par Folland, Gerald B. Publication : [S.l.] CRC Press 1995 . 276 p. , Abstract theory remains an indispensable foundation for the study of concrete cases. It shows what the general picture should look like and provides results that are useful again and again. Despite this, however, there are few, if any introductory texts that present a unified picture of the general abstract theory. A Course in Abstract Harmonic Analysis offers a concise, readable introduction to Fourier analysis on groups and unitary representation theory. After a brief review of the relevant parts of Banach algebra theory and spectral theory, the book proceeds to the basic facts about locally compact groups, Haar measure, and unitary representations, including the Gelfand-Raikov existence theorem. The author devotes two chapters to analysis on Abelian groups and compact groups, then explores induced representations, featuring the imprimitivity theorem and its applications. The book concludes with an informal discussion of some further aspects of the representation theory of non-compact, non-Abelian groups. 25 cm. Date : 1995 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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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),

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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),

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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),

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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),

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Additive subgroups of topological vector spaces par Banaszczyk, Wojciech Publication : Berlin | New York Springer-Verlag 1991 . vi, 178 pages 25 cm. Date : 1991 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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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),

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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),

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Analyse harmonique non-commutative sur certains espaces homogenes : etude de certaines integrales singulieres par Coifman, R. R. Publication : [S.l.] Springer 1972 . 168 p. 23 cm. Date : 1972 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Analysis on symmetric cones par Faraut, Jacques, Publication : Oxford | New York Clarendon Press ; | Oxford University Press, 1994 . xii, 382 p. 24 cm. Date : 1994 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Clifford algebras and Dirac operators in harmonic analysis / par Gilbert, John E. Publication : Cambridge [England] ; | New York : Cambridge University Press, 1991 . vi, 334 p. ; 23 cm. Date : 1991 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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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),

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Commuting nonselfadjoint operators in hilbert space : two independent studies par Livsic,, Moshe S. Publication : [S.l.] Springer 2008 . 118 p. , Classification of commuting non-selfadjoint operators is one of the most challenging problems in operator theory even in the finite-dimensional case. The spectral analysis of dissipative operators has led to a series of deep results in the framework of unitary dilations and characteristic operator functions. It has turned out that the theory has to be based on analytic functions on algebraic manifolds and not on functions of several independent variables as was previously believed. This follows from the generalized Cayley-Hamilton Theorem, due to M.S.Livsic: "Two commuting operators with finite dimensional imaginary parts are connected in the generic case, by a certain algebraic equation whose degree does not exceed the dimension of the sum of the ranges of imaginary parts." Such investigations have been carried out in two directions. One of them, presented by L.L.Waksman, is related to semigroups of projections of multiplication operators on Riemann surfaces. Another direction, which is presented here by M.S.Livsic is based on operator colligations and collective motions of systems. Every given wave equation can be obtained as an external manifestation of collective motions. The algebraic equation mentioned above is the corresponding dispersion law of the input-output waves. 24 cm. Date : 2008 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Geometric applications of Fourier series and spherical harmonics par Groemer, H. Publication : Cambridge Cambridge University Press 2009 . xi, 329 pages , Originally published: 1996. 25cm. Date : 2009 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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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),

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