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This book is devoted to the broad field of Fourier analysis and its applications to several areas of mathematics, including problems in the theory of pseudo-differential operators, partial differential equations, and time-frequency analysis. This collection of 20 refereed articles is based on selected talks given at the international conference “Fourier Analysis and Pseudo-Differential Operators,” June 25–30, 2012, at Aalto University, Finland, and presents the latest advances in the field. The conference was a satellite meeting of the 6th European Congress of Mathematics, which took place in Krakow in July 2012; it was also the 6th meeting in the series “Fourier Analysis and Partial Differential Equations.”.

Differential equations. --- Pseudodifferential operators. --- Fourier analysis --- Differential equations, Partial --- Mathematics --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Operations Research --- Calculus --- Fourier analysis. --- Numerical solutions. --- Analysis, Fourier --- Mathematics. --- Harmonic analysis. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Operator theory. --- Partial differential equations. --- Functions of real variables. --- Sequences (Mathematics). --- Partial Differential Equations. --- Global Analysis and Analysis on Manifolds. --- Operator Theory. --- Abstract Harmonic Analysis. --- Sequences, Series, Summability. --- Real Functions. --- Mathematical sequences --- Numerical sequences --- Algebra --- Real variables --- Functions of complex variables --- Partial differential equations --- Functional analysis --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Geometry, Algebraic --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Mathematical analysis --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Math --- Science --- Numerical analysis --- Differential equations, partial. --- Global analysis.

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Progress in Partial Differential Equations is devoted to modern topics in the theory of partial differential equations. It consists of both original articles and survey papers covering a wide scope of research topics in partial differential equations and their applications. The contributors were participants of the 8th ISAAC congress in Moscow in 2011 or are members of the PDE interest group of the ISAAC society. This volume is addressed to graduate students at various levels as well as researchers in partial differential equations and related fields. The reader will find this an excellent resource of both introductory and advanced material. The key topics are: • Linear hyperbolic equations and systems (scattering, symmetrisers) • Non-linear wave models (global existence, decay estimates, blow-up) • Evolution equations (control theory, well-posedness, smoothing) • Elliptic equations (uniqueness, non-uniqueness, positive solutions) • Special models from applications (Kirchhoff equation, Zakharov-Kuznetsov equation, thermoelasticity).

Mathematics --- Physical Sciences & Mathematics --- Calculus --- Differential equations. --- Differential equations, Partial. --- Partial differential equations --- 517.91 Differential equations --- Differential equations --- Mathematics. --- Dynamics. --- Ergodic theory. --- Partial differential equations. --- Mathematical physics. --- Partial Differential Equations. --- Ordinary Differential Equations. --- Dynamical Systems and Ergodic Theory. --- Mathematical Applications in the Physical Sciences. --- Mathematical Physics. --- Physical mathematics --- Physics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Math --- Science --- Differential equations, partial. --- Differential Equations. --- Differentiable dynamical systems. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics

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This monograph is devoted to the development of the theory of pseudo-di?erential n operators on spaces with symmetries. Such spaces are the Euclidean space R ,the n torus T , compact Lie groups and compact homogeneous spaces. The book consists of several parts. One of our aims has been not only to present new results on pseudo-di?erential operators but also to show parallels between di?erent approaches to pseudo-di?erential operators on di?erent spaces. Moreover, we tried to present the material in a self-contained way to make it accessible for readers approaching the material for the ?rst time. However, di?erent spaces on which we develop the theory of pseudo-di?er- tial operators require di?erent backgrounds. Thus, while operators on the - clidean space in Chapter 2 rely on the well-known Euclidean Fourier analysis, pseudo-di?erentialoperatorsonthetorusandmoregeneralLiegroupsinChapters 4 and 10 require certain backgrounds in discrete analysis and in the representation theory of compact Lie groups, which we therefore present in Chapter 3 and in Part III,respectively. Moreover,anyonewhowishestoworkwithpseudo-di?erential- erators on Lie groups will certainly bene?t from a good grasp of certain aspects of representation theory. That is why we present the main elements of this theory in Part III, thus eliminating the necessity for the reader to consult other sources for most of the time. Similarly, the backgrounds for the theory of pseudo-di?erential 3 operators on S and SU(2) developed in Chapter 12 can be found in Chapter 11 presented in a self-contained way suitable for immediate use.

Electronic books. -- local. --- Operator theory. --- Pseudodifferential operators. --- Pseudodifferential operators --- Mathematics --- Calculus --- Physical Sciences & Mathematics --- Operators, Pseudodifferential --- Pseudo-differential operators --- Mathematics. --- Algebra. --- Topological groups. --- Lie groups. --- Mathematical analysis. --- Analysis (Mathematics). --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Partial differential equations. --- Analysis. --- Partial Differential Equations. --- Topological Groups, Lie Groups. --- Global Analysis and Analysis on Manifolds. --- Partial differential equations --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- 517.1 Mathematical analysis --- Mathematical analysis --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Groups, Topological --- Continuous groups --- Math --- Science --- Operator theory --- Functional analysis --- Differential equations, partial. --- Topological Groups. --- Global analysis.

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This volume presents current trends in analysis and partial differential equations from researchers in developing countries. The fruit of the project 'Analysis in Developing Countries', whose aim was to bring together researchers from around the world, the volume also includes some contributions from researchers from developed countries. Focusing on topics in analysis related to partial differential equations, this volume contains selected contributions from the activities of the project at Imperial College London, namely the conference on Analysis and Partial Differential Equations held in September 2016 and the subsequent Official Development Assistance Week held in November 2016. Topics represented include Fourier analysis, pseudo-differential operators, integral equations, as well as related topics from numerical analysis and bifurcation theory, and the countries represented range from Burkina Faso and Ghana to Armenia, Kyrgyzstan and Tajikistan, including contributions from Brazil, Colombia and Cuba, as well as India and China. Suitable for postgraduate students and beyond, this volume offers the reader a broader, global perspective of contemporary research in analysis.

Differential equations, Partial. --- Mathematical analysis. --- Functional analysis. --- Partial differential equations. --- Fourier analysis. --- Functional Analysis. --- Partial Differential Equations. --- Fourier Analysis. --- Analysis, Fourier --- Mathematical analysis --- Partial differential equations --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations

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Progress in Partial Differential Equations is devoted to modern topics in the theory of partial differential equations. It consists of both original articles and survey papers covering a wide scope of research topics in partial differential equations and their applications. The contributors were participants of the 8th ISAAC congress in Moscow in 2011 or are members of the PDE interest group of the ISAAC society. This volume is addressed to graduate students at various levels as well as researchers in partial differential equations and related fields. The reader will find this an excellent resource of both introductory and advanced material. The key topics are: • Linear hyperbolic equations and systems (scattering, symmetrisers) • Non-linear wave models (global existence, decay estimates, blow-up) • Evolution equations (control theory, well-posedness, smoothing) • Elliptic equations (uniqueness, non-uniqueness, positive solutions) • Special models from applications (Kirchhoff equation, Zakharov-Kuznetsov equation, thermoelasticity).

Differential geometry. Global analysis --- Ergodic theory. Information theory --- Partial differential equations --- Differential equations --- Mathematics --- Mathematical physics --- differentiaalvergelijkingen --- differentiaal geometrie --- wiskunde --- fysica --- informatietheorie