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This book gives a friendly introduction to Fourier analysis on finite groups, both commutative and non-commutative. Aimed at students in mathematics, engineering and the physical sciences, it examines the theory of finite groups in a manner that is both accessible to the beginner and suitable for graduate research. With applications in chemistry, error-correcting codes, data analysis, graph theory, number theory and probability, the book presents a concrete approach to abstract group theory through applied examples, pictures and computer experiments. In the first part, the author parallels the development of Fourier analysis on the real line and the circle, and then moves on to analogues of higher dimensional Euclidean space. The second part emphasizes matrix groups such as the Heisenberg group of upper triangular 2x2 matrices. The book concludes with an introduction to zeta functions on finite graphs via the trace formula.

Finite groups. --- Fourier analysis. --- Analysis, Fourier --- Mathematical analysis --- Groups, Finite --- Group theory --- Modules (Algebra) --- #KVIV:BB --- Fourier analysis --- Finite groups

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This book surveys the application of the recently developed technique of the wavelet transform to a wide range of physical fields, including astrophysics, turbulence, meteorology, plasma physics, atomic and solid state physics, multifractals occurring in physics, biophysics (in medicine and physiology) and mathematical physics. The wavelet transform can analyze scale-dependent characteristics of a signal (or image) locally, unlike the Fourier transform, and more flexibly than the windowed Fourier transform developed by Gabor fifty years ago. The continuous wavelet transform is used mostly for analysis, but the discrete wavelet transform allows very fast compression and transmission of data and speeds up numerical calculation, and is applied, for example, in the solution of partial differential equations in physics. This book will be of interest to graduate students and researchers in many fields of physics, and to applied mathematicians and engineers interested in physical application.

Wavelets (Mathematics) --- Mathematical physics. --- Fourier transformations. --- Time measurements. --- Physical mathematics --- Physics --- Wavelet analysis --- Harmonic analysis --- Time --- Physical measurements --- Vibration --- Clocks and watches --- Transformations, Fourier --- Transforms, Fourier --- Fourier analysis --- Transformations (Mathematics) --- Mathematics --- Measurement

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Mathematical physics --- Wavelets (Mathematics) --- Fourier transformations. --- Time measurements. --- Mathematical physics. --- Wavelets (Mathematics). --- Physique mathématique --- Ondelettes --- Transformations de Fourier --- Temps --- Mesure

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Approximation et developpements --- Analyse de fourier --- Inegalite de jackson --- Inegalite de bernstein --- Ondelettes

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Operator theory --- C*-algebras --- Fourier analysis --- Hilbert space --- Representations of groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Banach spaces --- Hyperspace --- Inner product spaces --- Analysis, Fourier --- Mathematical analysis --- Algebras, C star --- Algebras, W star --- C star algebras --- W star algebras --- W*-algebras --- Banach algebras --- C*-algebras. --- Fourier analysis. --- Fourier, Analyse de --- Representations of groups. --- Représentations de groupes --- Hilbert space. --- Fourier, Analyse de. --- Représentations de groupes.