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Pseudo-Differential Operators, Generalized Functions and Asymptotics

2013-02-26 Mathematics
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Release : 2013-02-26
Genre : Mathematics
Kind : eBook
Book Rating : 853/5 ( reviews)

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Book Synopsis Pseudo-Differential Operators, Generalized Functions and Asymptotics by : Shahla Molahajloo

Download or read book Pseudo-Differential Operators, Generalized Functions and Asymptotics written by Shahla Molahajloo. This book was released on 2013-02-26. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of twenty peer-reviewed papers from the special session on pseudodifferential operators and the special session on generalized functions and asymptotics at the Eighth Congress of ISAAC held at the Peoples’ Friendship University of Russia in Moscow on August 22‒27, 2011. The category of papers on pseudo-differential operators contains such topics as elliptic operators assigned to diffeomorphisms of smooth manifolds, analysis on singular manifolds with edges, heat kernels and Green functions of sub-Laplacians on the Heisenberg group and Lie groups with more complexities than but closely related to the Heisenberg group, Lp-boundedness of pseudo-differential operators on the torus, and pseudo-differential operators related to time-frequency analysis. The second group of papers contains various classes of distributions and algebras of generalized functions with applications in linear and nonlinear differential equations, initial value problems and boundary value problems, stochastic and Malliavin-type differential equations. This second group of papers are related to the third collection of papers via the setting of Colombeau-type spaces and algebras in which microlocal analysis is developed by means of techniques in asymptotics. The volume contains the synergies of the three areas treated and is a useful complement to volumes 155, 164, 172, 189, 205 and 213 published in the same series in, respectively, 2004, 2006, 2007, 2009, 2010 and 2011.

Pseudo-Differential Operators and Generalized Functions

2015-04-27 Mathematics
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Release : 2015-04-27
Genre : Mathematics
Kind : eBook
Book Rating : 181/5 ( reviews)

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Book Synopsis Pseudo-Differential Operators and Generalized Functions by : Stevan Pilipović

Download or read book Pseudo-Differential Operators and Generalized Functions written by Stevan Pilipović. This book was released on 2015-04-27. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers peer-reviewed contributions representing modern trends in the theory of generalized functions and pseudo-differential operators. It is dedicated to Professor Michael Oberguggenberger (Innsbruck University, Austria) in honour of his 60th birthday. The topics covered were suggested by the ISAAC Group in Generalized Functions (GF) and the ISAAC Group in Pseudo-Differential Operators (IGPDO), which met at the 9th ISAAC congress in Krakow, Poland in August 2013. Topics include Columbeau algebras, ultra-distributions, partial differential equations, micro-local analysis, harmonic analysis, global analysis, geometry, quantization, mathematical physics, and time-frequency analysis. Featuring both essays and research articles, the book will be of great interest to graduate students and researchers working in analysis, PDE and mathematical physics, while also offering a valuable complement to the volumes on this topic previously published in the OT series.

Pseudo-Differential Operators on Manifolds with Singularities

1991-10-17 Mathematics
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Release : 1991-10-17
Genre : Mathematics
Kind : eBook
Book Rating : 459/5 ( reviews)

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Book Synopsis Pseudo-Differential Operators on Manifolds with Singularities by : B.-W. Schulze

Download or read book Pseudo-Differential Operators on Manifolds with Singularities written by B.-W. Schulze. This book was released on 1991-10-17. Available in PDF, EPUB and Kindle. Book excerpt: The analysis of differential equations in domains and on manifolds with singularities belongs to the main streams of recent developments in applied and pure mathematics. The applications and concrete models from engineering and physics are often classical but the modern structure calculus was only possible since the achievements of pseudo-differential operators. This led to deep connections with index theory, topology and mathematical physics. The present book is devoted to elliptic partial differential equations in the framework of pseudo-differential operators. The first chapter contains the Mellin pseudo-differential calculus on R+ and the functional analysis of weighted Sobolev spaces with discrete and continuous asymptotics. Chapter 2 is devoted to the analogous theory on manifolds with conical singularities, Chapter 3 to manifolds with edges. Employed are pseudo-differential operators along edges with cone-operator-valued symbols.

Generalized Functions and Fourier Analysis

2017-05-06 Mathematics
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Release : 2017-05-06
Genre : Mathematics
Kind : eBook
Book Rating : 115/5 ( reviews)

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Book Synopsis Generalized Functions and Fourier Analysis by : Michael Oberguggenberger

Download or read book Generalized Functions and Fourier Analysis written by Michael Oberguggenberger. This book was released on 2017-05-06. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an excellent and up-to-date overview on the convergence and joint progress in the fields of Generalized Functions and Fourier Analysis, notably in the core disciplines of pseudodifferential operators, microlocal analysis and time-frequency analysis. The volume is a collection of chapters addressing these fields, their interaction, their unifying concepts and their applications and is based on scientific activities related to the International Association for Generalized Functions (IAGF) and the ISAAC interest groups on Pseudo-Differential Operators (IGPDO) and on Generalized Functions (IGGF), notably on the longstanding collaboration of these groups within ISAAC.

Pseudo-Differential Operators: Partial Differential Equations and Time-Frequency Analysis

2007 Mathematics
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Release : 2007
Genre : Mathematics
Kind : eBook
Book Rating : 765/5 ( reviews)

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Book Synopsis Pseudo-Differential Operators: Partial Differential Equations and Time-Frequency Analysis by : Luigi Rodino

Download or read book Pseudo-Differential Operators: Partial Differential Equations and Time-Frequency Analysis written by Luigi Rodino. This book was released on 2007. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on lectures given at the workshop on pseudo-differential operators held at the Fields Institute from December 11, 2006 to December 15, 2006. The two main themes of the workshop and hence this volume are partial differential equations and time-frequency analysis. The contents of this volume consist of five mini-courses for graduate students and post-docs, and fifteen papers on related topics. Of particular interest in this volume are the mathematical underpinnings, applications and ramifications of the relatively new Stockwell transform, which is a hybrid of the Gabor transform and the wavelet transform. The twenty papers in this volume reflect modern trends in the development of pseudo-differential operators.

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