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Harmonic analysis. Fourier analysis --- Harmonic analysis --- 51 --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- 51 Mathematics --- Congresses --- Harmonic analysis - Congresses.

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Manifolds over complete nonarchimedean fields together with notions like tangent spaces and vector fields form a convenient geometric language to express the basic formalism of p-adic analysis. The volume starts with a self-contained and detailed introduction to this language. This includes the discussion of spaces of locally analytic functions as topological vector spaces, important for applications in representation theory. The author then sets up the analytic foundations of the theory of p-adic Lie groups and develops the relation between p-adic Lie groups and their Lie algebras. The second part of the book contains, for the first time in a textbook, a detailed exposition of Lazard's algebraic approach to compact p-adic Lie groups, via his notion of a p-valuation, together with its application to the structure of completed group rings.

Harmonic analysis -- Congresses. --- Harmonic analysis. --- p-adic groups -- Congresses. --- p-adic groups. --- Representations of Lie groups -- Congresses. --- Representations of Lie groups. --- Lie groups --- p-adic groups --- p-adic analysis --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Calculus --- Lie groups. --- Lie algebras. --- Algebras, Lie --- Groups, Lie --- Mathematics. --- Associative rings. --- Rings (Algebra). --- Topological groups. --- Topological Groups, Lie Groups. --- Associative Rings and Algebras. --- Lie algebras --- Symmetric spaces --- Topological groups --- Algebra, Abstract --- Algebras, Linear --- Topological Groups. --- Algebra. --- Mathematical analysis --- Groups, Topological --- Continuous groups --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra)

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This is a collection of papers by participants at the High Dimensional Probability VI Meeting held from October 9-14, 2011 at the Banff International Research Station in Banff, Alberta, Canada.  High Dimensional Probability (HDP) is an area of mathematics that includes the study of probability distributions and limit theorems in infinite dimensional spaces such as Hilbert spaces and Banach spaces. The most remarkable feature of this area is that it has resulted in the creation of powerful new tools and perspectives, whose range of application has led to interactions with other areas of mathematics, statistics, and computer science. These include random matrix theory, nonparametric statistics, empirical process theory, statistical learning theory, concentration of measure phenomena, strong and weak approximations, distribution function estimation in high dimensions, combinatorial optimization, and random graph theory. The papers in this volume show that HDP theory continues to develop new tools, methods, techniques and perspectives to analyze the random phenomena. Both researchers and advanced students will find this book of great use for learning about new avenues of research.

Differential equations, Partial -- Congresses. --- Harmonic analysis -- Congresses. --- Probabilities -- Congresses. --- Stochastic analysis -- Congresses. --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Probabilities. --- Linear topological spaces. --- Topological linear spaces --- Topological vector spaces --- Vector topology --- Probability --- Statistical inference --- Mathematics. --- Computer science --- Computer mathematics. --- Calculus of variations. --- Probability Theory and Stochastic Processes. --- Mathematical Applications in Computer Science. --- Calculus of Variations and Optimal Control; Optimization. --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Topology --- Vector spaces --- Distribution (Probability theory. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Computer science—Mathematics. --- Isoperimetrical problems --- Variations, Calculus of --- Computer mathematics --- Electronic data processing

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Recent Advances in Harmonic Analysis and Applications is dedicated to the 65th birthday of Konstantin Oskolkov and features contributions from analysts around the world.   The volume contains expository articles by leading experts in their fields, as well as selected high quality research papers that explore new results and trends in classical and computational harmonic analysis, approximation theory, combinatorics, convex analysis, differential equations, functional analysis, Fourier analysis, graph theory, orthogonal polynomials, special functions, and trigonometric series.   Numerous articles in the volume emphasize remarkable connections between harmonic analysis and other seemingly unrelated areas of mathematics, such as the interaction between abstract problems in additive number theory, Fourier analysis, and experimentally discovered optical phenomena in physics. Survey and research articles provide an up-to-date account of various vital directions of modern analysis and will in particular be of interest to young researchers who are just starting their career. This book will also be useful to experts in analysis, discrete mathematics, physics, signal processing, and other areas of science.

Differential equations, Partial -- Congresses. --- Harmonic analysis -- Congresses. --- Harmonic analysis. --- Harmonic analysis --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Partial differential equations. --- Algorithms. --- Number theory. --- Abstract Harmonic Analysis. --- Partial Differential Equations. --- Number Theory. --- Analysis. --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Number study --- Numbers, Theory of --- Algebra --- Algorism --- Arithmetic --- Partial differential equations --- 517.1 Mathematical analysis --- Math --- Science --- Foundations --- Differential equations, partial. --- Global analysis (Mathematics). --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Oskolkov, Konstantin Ilyich,

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Connects scientific understandings of acoustics with practical applications to musical performance. Of central importance are the tonal characteristics of musical instruments and the singing voice including detailed representations of directional characteristics. Furthermore, room acoustical concerns related to concert halls and opera houses are considered. Based on this, suggestions are made for musical performance. Included are seating arrangements within the orchestra and adaptation of performance techniques to the performance environment. This presentation dispenses with complicated mathematical connections and aims for conceptual explanations accessible to musicians, particularly for conductors. The graphical representations of the directional dependence of sound radiation by musical instruments and the singing voice are unique. This German edition has become a standard reference work for audio engineers and scientists.

Acoustical engineering. --- Conducting. --- Harmonic analysis --Congresses. --- Lie algebras --Congresses. --- Lie groups --Congresses. --- Music --Acoustics and physics. --- Music --Performance. --- Theaters --Acoustic properties. --- Music --- Acoustical engineering --- Conducting --- Theaters --- Acoustics & Sound --- Music Philosophy --- Physics --- Music, Dance, Drama & Film --- Physical Sciences & Mathematics --- Acoustics and physics --- Performance --- Acoustic properties --- Acoustics and physics. --- Performance. --- Acoustic properties. --- Opera-houses --- Playhouses (Theaters) --- Theatres --- Acoustic engineering --- Sonic engineering --- Sonics --- Sound engineering --- Sound-waves --- Musical acoustics --- Musical performance --- Performance of music --- Band conducting --- Conducting (Music) --- Music conducting --- Orchestra conducting --- Industrial applications --- Physics. --- Acoustics. --- Engineering Acoustics. --- 517 <061.3> --- 517.9 --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- 517 <061.3> Analysis--?<061.3> --- Analysis--?<061.3> --- Harmonic analysis. Fourier analysis --- Ergodic theory. Information theory --- 519.2 --- 519.2 Probability. Mathematical statistics --- Probability. Mathematical statistics --- Engineering --- Arts facilities --- Auditoriums --- Centers for the performing arts --- Music-halls --- Sound --- Monochord --- Harmonic analysis --- Lie algebras --- Lie groups --- Congresses. --- Ergodic theory --- Topological dynamics --- Acoustics in engineering. --- Théorie ergodique --- Théorie ergodique. --- Systèmes dynamiques --- Systèmes dynamiques --- Théorie ergodique --- Analyse harmonique