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This volume contains the proceedings of the conferences held in the second half of the Special Year in Harmonic Analysis and Operator Algebras at the Centre for Mathematical Analysis in 1987. There were in fact two conferences, the first held in August and the second somewhat smaller gathering in December.
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This volume contains the proceedings of the International Conference on Harmonic Analysis and Related Topics held at Macquarie University, Sydney, from January 14-18, 2002. The conference celebrated the many significant achievements and contributions to mathematics of Professor Alan G.
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Ergodic theory is a field that is stimulating on its own, and also in its interactions with other branches of mathematics and science. In recent years, the interchanges with harmonic analysis have been especially noticeable and productive. This book contains survey papers describing the relationship of ergodic theory with convergence, rigidity theory and the theory of joinings. These papers present the background of each area of interaction, the most outstanding results and promising lines of research. They should form perfect starting points for anyone beginning research in one of these areas. Thirteen related research papers describe the work; several treat questions arising from the Furstenberg multiple recurrence theory, while the remainder deal with convergence and a variety of other topics in dynamics.
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This book captures the essence of the current state of research in wavelet analysis and its applications, and identifies the changes and opportunities - both current and future in the field. Distinguished researchers such as Prof John Daugman from Cambridge University and Prof Victor Wickerhauser from Washington University present their research papers.
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Wavelet analysis and its applications have been one of the fastest- growing research areas in the past several years. Wavelet theory has been employed in numerous fields and applications, such as signal and image processing, communication systems, biomedical imaging, radar, and air acoustics.
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The wavelet is a powerful mathematical tool that plays an important role in science and technology. This book looks at some of the most creative and popular applications of wavelets including biomedical signal processing, image processing, communication signal processing, Internet of Things (IoT), acoustical signal processing, financial market data analysis, energy and power management, and COVID.
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In 1987, the Centre for Mathematical Analysis ran a Special Year on Harmonic Analysis and Operator Algebras. Most of the activity involved was concentrated in that period from May to August, and in November and December; during this time the Centre was overrun with people with disparate interests, ranging through classical Harmonic Analysis, Representation Theory, Operator Algebras, Ergodic Theory, Number Theory, Non-commutative Topology, and Mathematical Physics; at the same time, the Centre's usual program in Partial Differential Equations, Functional Analysis and Numerical Analysis was under way. Space was a problem, but this had its positive aspects too, as persons with different interests, thrown together by fate in the same office, ended up chatting with each other. Apart from informal discussions and regular and spontaneous seminars, two mini-conferences were held in the May to August period, in the (forlorn) hope that all the visitors would get a chance to speak at one or the other of these, if not both. This is the result of the first of these mini-conferences.
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The mutual influence between mathematics and science and technology is becoming more and more widespread with profound connections among them being discovered. In particular, important connections between harmonic analysis, wavelet analysis and p-adic analysis have been found recently. This volume reports these findings and guides the reader towards the latest areas for further research. It is divided into two parts: harmonic, wavelet and p-adic analysis and p-adic and stochastic analysis.
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This book presents a mathematical introduction to the theory of orthogonal wavelets and their uses in analysing functions and function spaces, both in one and in several variables. Starting with a detailed and self contained discussion of the general construction of one dimensional wavelets from multiresolution analysis, the book presents in detail the most important wavelets: spline wavelets, Meyer's wavelets and wavelets with compact support. It then moves to the corresponding multivariable theory and gives genuine multivariable examples. Wavelet decompositions in Lp spaces, Hardy spaces and Besov spaces are discussed and wavelet characterisations of those spaces are provided. Also included are some additional topics like periodic wavelets or wavelets not associated with a multiresolution analysis. This will be an invaluable book for those wishing to learn about the mathematical foundations of wavelets.
Wavelets (Mathematics) --- Wavelet analysis --- Harmonic analysis
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