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Pseudodifferential operators.

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This volume consists of papers inspired by the special session on pseudo-differential operators at the 10th ISAAC Congress held at the University of Macau, August 3-8, 2015 and the mini-symposium on pseudo-differential operators in industries and technologies at the 8th ICIAM held at the National Convention Center in Beijing, August 10-14, 2015. The twelve papers included present cutting-edge trends in pseudo-differential operators and applications from the perspectives of Lie groups (Chapters 1-2), geometry (Chapters 3-5) and applications (Chapters 6-12). Many contributions cover applications in probability, differential equations and time-frequency analysis. A focus on the synergies of pseudo-differential operators with applications, especially real-life applications, enhances understanding of the analysis and the usefulness of these operators.

Mathematics. --- Operator theory. --- Partial differential equations. --- Information theory. --- Differential geometry. --- Probabilities. --- Operator Theory. --- Partial Differential Equations. --- Differential Geometry. --- Probability Theory and Stochastic Processes. --- Information and Communication, Circuits. --- Pseudodifferential operators. --- Operators, Pseudodifferential --- Pseudo-differential operators --- Operator theory --- Differential equations, partial. --- Global differential geometry. --- Distribution (Probability theory. --- Math --- Science --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Geometry, Differential --- Partial differential equations --- Functional analysis --- Communication theory --- Communication --- Cybernetics --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Differential geometry --- Differential equations, Partial. --- Geometry, Differential.

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This textbook presents basic notions and techniques of Fourier analysis in discrete settings. Written in a concise style, it is interlaced with remarks, discussions and motivations from signal analysis.   The first part is dedicated to topics related to the Fourier transform, including discrete time-frequency analysis and discrete wavelet analysis. Basic knowledge of linear algebra and calculus is the only prerequisite. The second part is built on Hilbert spaces and Fourier series and culminates in a section on pseudo-differential operators, providing a lucid introduction to this advanced topic in analysis. Some measure theory language is used, although most of this part is accessible to students familiar with an undergraduate course in real analysis.   Discrete Fourier Analysis is aimed at advanced undergraduate and graduate students in mathematics and applied mathematics. Enhanced with exercises, it will be an excellent resource for the classroom as well as for self-study.

Harmonic analysis. Fourier analysis --- Partial differential equations --- Mathematical analysis --- Numerical analysis --- Fourieranalyse --- differentiaalvergelijkingen --- Fourierreeksen --- mathematische modellen --- numerieke analyse

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This volume consists of eighteen peer-reviewed papers related to lectures on pseudo-differential operators presented at the meeting of the ISAAC Group in Pseudo-Differential Operators (IGPDO) held at Imperial College London on July 13-18, 2009. Featured in this volume are the analysis, applications and computations of pseudo-differential operators in mathematics, physics and signal analysis. This volume is a useful complement to the volumes Advances in Pseudo-Differential Operators , Pseudo-Differential Operators and Related Topics , Modern Trends in Pseudo-Differential Operators , New Developments in Pseudo-Differential Operators  and Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations  published in the same series in, respectively, 2004, 2006, 2007, 2009 and 2010.

Geometry --- Operator theory --- Partial differential equations --- Electrical engineering --- Applied physical engineering --- differentiaalvergelijkingen --- elektrotechniek --- geometrie

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The ISAAC Group in Pseudo-di?erential Operators (IGPDO) was formed at the Fourth ISAAC Congress held at York University in Toronto in 2003 and the ?rst volume entitled Advances in Pseudo-di?erential Operators and devoted to papers focussing on pseudo-di?erential operators and its diverse applications was then initiated and published in Professor Israel Gohberg's series Operator Theory: - vances and Applications in 2004. As a satellite conference to the Fourth Congress of European Mathematics held at Stockholm University in 2004,the International ConferenceonPseudo-di?erentialOperatorsandRelatedTopicswasheldatVaxj ¨ o ¨ University in Sweden. Prompted by the enthusiasm of the participants, the second volume with similar scope and entitled Pseudo-di?erential Operators and Related Topics was published in the same series in 2006. Members of IGPDO met again at the Fifth ISAAC Congress held at Univ- sit` a di Catania in Italy in July 2005. Core members of the group encouraged the publication of a sequel to the Toronto Volume and the Vaxj ¨ o ¨ Volume. The vision is to seek new directionsfor the broadsubjectonpseudo-di?erentialoperatorsand the strategy is to devote the Catania Volume not only to papers based on lectures given at the special session on pseudo-di?erential operators, but also invited - pers that bear on the themes of IGPDO. In order to re?ect the goal and vision of IGPDO, the Catania Volume is entitled Modern Trends in Pseudo-di?erential Operators.

Differential geometry. Global analysis --- Operator theory --- Partial differential equations --- differentiaalvergelijkingen --- analyse (wiskunde) --- differentiaal geometrie