Pseudo-Differential Operators on Manifolds with Singularities

Pseudo-Differential Operators on Manifolds with Singularities PDF

Author: B.-W. Schulze

Publisher: Elsevier

Published: 1991-10-17

Total Pages: 417

ISBN-13: 0080875459

DOWNLOAD EBOOK →

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.

Pseudo-Differential Operators, Singularities, Applications

Pseudo-Differential Operators, Singularities, Applications PDF

Author: Iouri Egorov

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 360

ISBN-13: 3034889003

DOWNLOAD EBOOK →

This book grew out of lecture notes based on the DMV seminar "Pseudo- Differential Operators, Singularities, Applications" held by the authors in Reisenburg-Günzburg, 12–19 July 1992. The modern theory of elliptic boundary value problems in domains having conical or edge singularities on the boundary as well as the classical theory of elliptic boundary value problems and the original Kondratiev theory are presented. This material forms the foundation for the second part of the book which contains a new construction of pseudo-differential operators with symbols corresponding to the singularities of the boundary of different dimensions. This allows in particular to obtain complete asymptotic expansions of solutions near these singularities.

Pseudo-Differential Operators, Generalized Functions and Asymptotics

Pseudo-Differential Operators, Generalized Functions and Asymptotics PDF

Author: Shahla Molahajloo

Publisher: Springer Science & Business Media

Published: 2013-02-26

Total Pages: 371

ISBN-13: 3034805853

DOWNLOAD EBOOK →

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

Pseudo-differential Operators PDF

Author: Louis Nirenberg

Publisher: Springer Science & Business Media

Published: 2011-06-06

Total Pages: 363

ISBN-13: 3642110746

DOWNLOAD EBOOK →

S. Agmon: Asymptotic formulas with remainder estimates for eigenvalues of elliptic operators.- J. Bokobza-Haggiag: Une définition globale des opérateurs pseudo-différentiels sur une variété différentiable.- L. Boutet de Monvel: Pseudo-differential operators and analytic function.- A. Calderon: A priori estimates for singular integral operators.- B.F. Jones: Characterization of spaces of Bessel potentials related to the heat equation.- J.J. Kohn: Pseudo-differential operators and non-elliptic problems.- R.T. Seeley: Topics in pseudo-differential operators.- I.M. E. Shamir: Boundary value problems for elliptic convolution systems.- Singer: Elliptic operators on manifolds.

Lectures on Pseudo-Differential Operators

Lectures on Pseudo-Differential Operators PDF

Author: Alexander Nagel

Publisher: Princeton University Press

Published: 2015-03-08

Total Pages: 167

ISBN-13: 1400870488

DOWNLOAD EBOOK →

The theory of pseudo-differential operators (which originated as singular integral operators) was largely influenced by its application to function theory in one complex variable and regularity properties of solutions of elliptic partial differential equations. Given here is an exposition of some new classes of pseudo-differential operators relevant to several complex variables and certain non-elliptic problems. Originally published in 1979. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

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

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

Author: Luigi Rodino

Publisher: American Mathematical Soc.

Published: 2007

Total Pages: 426

ISBN-13: 0821842765

DOWNLOAD EBOOK →

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.

Elliptic Theory on Singular Manifolds

Elliptic Theory on Singular Manifolds PDF

Author: Vladimir E. Nazaikinskii

Publisher: CRC Press

Published: 2005-08-12

Total Pages: 372

ISBN-13: 1420034979

DOWNLOAD EBOOK →

The analysis and topology of elliptic operators on manifolds with singularities are much more complicated than in the smooth case and require completely new mathematical notions and theories. While there has recently been much progress in the field, many of these results have remained scattered in journals and preprints. Starting from an ele

Lanterna Rally - Theme by Grace Themes