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The current book makes several useful topics from the theory of special functions, in particular the theory of spherical harmonics and Legendre polynomials in arbitrary dimensions, available to undergraduates studying physics or mathematics. With this audience in mind, nearly all details of the calculations and proofs are written out, and extensive background material is covered before exploring the main subject matter. Contents: Introduction and Motivation; Working in p Dimensions; Orthogonal Polynomials; Spherical Harmonics in p Dimensions; Solutions to Problems. Readership: Undergraduate an

Spherical harmonics. --- Spherical functions. --- Legendre's polynomials. --- Mathematical physics. --- Physical mathematics --- Physics --- Functions, Spherical --- Spherical harmonics --- Transcendental functions --- Spheroidal functions --- Functions, Potential --- Potential functions --- Harmonic analysis --- Harmonic functions --- Polynomials, Legendre's --- Orthogonal polynomials --- Mathematics

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This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respective generalizations to non-abelian groups, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelic groups, as well as a complementary section on direct and projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonic analysis and for researchers seeking to apply it.

Mathematics. --- Harmonic analysis. --- Applied mathematics. --- Engineering mathematics. --- Visualization. --- Abstract Harmonic Analysis. --- Applications of Mathematics. --- Visualisation --- Imagery (Psychology) --- Imagination --- Visual perception --- Engineering --- Engineering analysis --- Mathematical analysis --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Math --- Science

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This text is addressed to graduate students in mathematics and to interested researchers who wish to acquire an in depth understanding of Euclidean Harmonic analysis. The text covers modern topics and techniques in function spaces, atomic decompositions, singular integrals of nonconvolution type, and the boundedness and convergence of Fourier series and integrals. The exposition and style are designed to stimulate further study and promote research. Historical information and references are included at the end of each chapter. This third edition includes a new chapter entitled "Multilinear Harmonic Analysis" which focuses on topics related to multilinear operators and their applications. Sections 1.1 and 1.2 are also new in this edition. Numerous corrections have been made to the text from the previous editions and several improvements have been incorporated, such as the adoption of clear and elegant statements. A few more exercises have been added with relevant hints when necessary. Reviews from the Second Edition: “The books cover a large amount of mathematics. They are certainly a valuable and useful addition to the existing literature and can serve as textbooks or as reference books. Students will especially appreciate the extensive collection of exercises.” —Andreas Seeger, Mathematical Reviews “The exercises at the end of each section supplement the material of the section nicely and provide a good chance to develop additional intuition and deeper comprehension. The historical notes in each chapter are intended to provide an account of past research as well as to suggest directions for further investigation. The volume is mainly addressed to graduate students who wish to study harmonic analysis.” —Leonid Golinskii, zbMATH.

Mathematics. --- Harmonic analysis. --- Fourier analysis. --- Functional analysis. --- Fourier Analysis. --- Abstract Harmonic Analysis. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Analysis, Fourier --- Mathematical analysis --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis

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Probability theory on compact Lie groups deals with the interaction between “chance” and “symmetry,” a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applications in statistics and engineering (particularly with respect to signal processing). The author gives a comprehensive introduction to some of the principle areas of study, with an emphasis on applicability. The most important topics presented are: the study of measures via the non-commutative Fourier transform, existence and regularity of densities, properties of random walks and convolution semigroups of measures, and the statistical problem of deconvolution. The emphasis on compact (rather than general) Lie groups helps readers to get acquainted with what is widely seen as a difficult field but which is also justified by the wealth of interesting results at this level and the importance of these groups for applications. The book is primarily aimed at researchers working in probability, stochastic analysis and harmonic analysis on groups. It will also be of interest to mathematicians working in Lie theory and physicists, statisticians and engineers who are working on related applications. A background in first year graduate level measure theoretic probability and functional analysis is essential; a background in Lie groups and representation theory is certainly helpful but the first two chapters also offer orientation in these subjects.

Lie groups. --- Mathematics. --- Fourier analysis. --- Math --- Science --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Analysis, Fourier --- Mathematical analysis --- Distribution (Probability theory. --- Harmonic analysis. --- Topological Groups. --- Functional analysis. --- Probability Theory and Stochastic Processes. --- Abstract Harmonic Analysis. --- Topological Groups, Lie Groups. --- Functional Analysis. --- Fourier Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Groups, Topological --- Continuous groups --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probabilities. --- Topological groups. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk

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This book provides a survey on wide-spread of employing wavelets analysis  in different applications of speech processing. The author examines development and research in different application of speech processing. The book also summarizes the state of the art research on wavelet in speech processing.

Speech processing systems. --- Harmonic analysis. --- Telecommunication. --- Wavelets (Mathematics) --- Wavelet analysis --- Electric communication --- Mass communication --- Telecom --- Telecommunication industry --- Telecommunications --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Engineering. --- Electrical engineering. --- Signal, Image and Speech Processing. --- Communications Engineering, Networks. --- Abstract Harmonic Analysis. --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Electric engineering --- Engineering --- Construction --- Industrial arts --- Technology --- Harmonic analysis --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Communication --- Telecommuting --- Signal processing. --- Image processing. --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication)