Pseudo Differential Operators On Manifolds With Singularities

Author : B.-W. Schulze
Publisher : Elsevier
Page : 417 pages
File Size : 45,9 Mb
Release : 1991-10-17
Category : Mathematics
ISBN : 9780080875453

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Pseudo-Differential Operators on Manifolds with Singularities by B.-W. Schulze Pdf

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.

Author : Iouri Egorov,Bert-Wolfgang Schulze
Publisher : Birkhäuser
Page : 360 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034889001

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Pseudo-Differential Operators, Singularities, Applications by Iouri Egorov,Bert-Wolfgang Schulze Pdf

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.

Author : Christoph Dorschfeldt
Publisher : Wiley-VCH
Page : 208 pages
File Size : 41,8 Mb
Release : 1998-09-16
Category : Mathematics
ISBN : STANFORD:36105021325753

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Algebras of Pseudodifferential Operators Near Edge and Corner Singularities by Christoph Dorschfeldt Pdf

This research monograph deals with analysis on manifolds with singularities. More precisely, it presents pseudodifferential operators near edges and corners. In particular, it considers parameter-dependent edge operators and edge operators of Mellin type. The investigation of such operator families is necessary to construct operator algebras on manifolds with higher singularities. A self-contained exposition in Mellin techniques and pseudodifferential operators with operator-valued symbols is given. The algebra of parameter-dependent edge operators is constructed. Finally, Mellin operators near corner singularities are investigated. The focus is on elliptic theory. Elliptic operators on manifolds with edges are constructed as well as parametrices to elliptic elements. The equivalence of ellipticity and the Fredholm property is shown. Close to corner singularities, edge operators of Mellin type are defined, a pseudodifferential calculus is presented and parametrices are constructed. Asymptotics are treated using analytic functions and the concept of continuous asymptotic types.

Author : Ryuichi Ashino,Paolo Boggiatto,Man-Wah Wong
Publisher : Birkhäuser
Page : 236 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034878401

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Advances in Pseudo-Differential Operators by Ryuichi Ashino,Paolo Boggiatto,Man-Wah Wong Pdf

This volume consists of the plenary lectures and invited talks in the special session on pseudo-differential operators given at the Fourth Congress of the International Society for Analysis, Applications and Computation (ISAAC) held at York University in Toronto, August 11-16, 2003. The theme is to look at pseudo-differential operators in a very general sense and to report recent advances in a broad spectrum of topics, such as pde, quantization, filters and localization operators, modulation spaces, and numerical experiments in wavelet transforms and orthonormal wavelet bases.

Author : Luigi Rodino,Bert-Wolfgang Schulze,Man Wah Wong
Publisher : American Mathematical Soc.
Page : 432 pages
File Size : 43,5 Mb
Release : 2007-11-21
Category : Mathematics
ISBN : 0821871552

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Pseudo-differential Operators by Luigi Rodino,Bert-Wolfgang Schulze,Man Wah Wong Pdf

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.

Author : M. W. Wong,Hongmei Zhu
Publisher : Birkhäuser
Page : 239 pages
File Size : 42,9 Mb
Release : 2017-01-20
Category : Mathematics
ISBN : 9783319475127

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Pseudo-Differential Operators: Groups, Geometry and Applications by M. W. Wong,Hongmei Zhu Pdf

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.

Author : Luigi Rodino,M. W. Wong
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 47,8 Mb
Release : 2009-01-06
Category : Mathematics
ISBN : 9783764389697

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New Developments in Pseudo-Differential Operators by Luigi Rodino,M. W. Wong Pdf

This volume consists of peer-reviewed papers related to lectures on pseudo-differential operators presented at the meeting of the ISAAC Group in Pseudo-Differential Operators (IGPDO) held on August 13-18, 2007, and invited papers by experts in the field.

Author : Luigi Rodino,M. W. Wong,Hongmei Zhu
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 53,5 Mb
Release : 2011-03-14
Category : Mathematics
ISBN : 9783034800495

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Pseudo-Differential Operators: Analysis, Applications and Computations by Luigi Rodino,M. W. Wong,Hongmei Zhu Pdf

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.

Author : Boris Plamenevskii,Oleg Sarafanov
Publisher : Springer Nature
Page : 249 pages
File Size : 44,8 Mb
Release : 2023-05-04
Category : Mathematics
ISBN : 9783031283987

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Solvable Algebras of Pseudodifferential Operators by Boris Plamenevskii,Oleg Sarafanov Pdf

This book presents original research results on pseudodifferential operators. C*-algebras generated by pseudodifferential operators with piecewise smooth symbols on a smooth manifold are considered. For each algebra, all the equivalence classes of irreducible representations are listed; as a consequence, a criterion for a pseudodifferential operator to be Fredholm is stated, the topology on the spectrum is described, and a solving series is constructed. Pseudodifferential operators on manifolds with edges are introduced, their properties are considered in details, and an algebra generated by the operators is studied. An introductory chapter includes all necessary preliminaries from the theory of pseudodifferential operators and C*-algebras.

Author : Shahla Molahajloo,M. W. Wong
Publisher : Springer
Page : 257 pages
File Size : 52,9 Mb
Release : 2019-05-08
Category : Mathematics
ISBN : 9783030051686

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Analysis of Pseudo-Differential Operators by Shahla Molahajloo,M. W. Wong Pdf

This volume, like its predecessors, is based on the special session on pseudo-differential operators, one of the many special sessions at the 11th ISAAC Congress, held at Linnaeus University in Sweden on August 14-18, 2017. It includes research papers presented at the session and invited papers by experts in fields that involve pseudo-differential operators. The first four chapters focus on the functional analysis of pseudo-differential operators on a spectrum of settings from Z to Rn to compact groups. Chapters 5 and 6 discuss operators on Lie groups and manifolds with edge, while the following two chapters cover topics related to probabilities. The final chapters then address topics in differential equations.

Author : Michael Demuth,Bert-Wolfgang Schulze
Publisher : Birkhäuser
Page : 422 pages
File Size : 44,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034890922

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Partial Differential Operators and Mathematical Physics by Michael Demuth,Bert-Wolfgang Schulze Pdf

The book contains the contributions to the conference on "Partial Differential Equations" held in Holzhau (Germany) in July 1994, where outstanding specialists from analysis, geometry and mathematical physics reviewed recent progress and new interactions in these areas. Topics of special interest at the conference and which now form the core of this volume are hyperbolic operators, spectral theory for elliptic operators, eta-invariant, singular configura- tions and asymptotics, Bergman-kernel, attractors of non-autonomous evolution equations, pseudo-differential boundary value problems, Mellin pseudo- differential operators, approximation and stability problems for elliptic operators, and operator determinants. In spectral theory adiabatic and semiclassical limits, Dirichlet decoupling and domain perturbations, capacity of obstacles, limiting absorption problems, N-body scattering, and number of bound states are considered. Schrödinger operators are studied with magnetic fields, with random and with many-body potentials, and for nonlinear problems. In semigroup theory the Feller property, errors for product formulas, fractional powers of generators, and functional integration for relativistic semigroups are analyzed.

Author : Vladimir E. Nazaikinskii,Anton Yu. Savin,Bert-Wolfgang Schulze,Boris Yu. Sternin
Publisher : CRC Press
Page : 372 pages
File Size : 42,5 Mb
Release : 2005-08-12
Category : Mathematics
ISBN : 9781420034974

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Elliptic Theory on Singular Manifolds by Vladimir E. Nazaikinskii,Anton Yu. Savin,Bert-Wolfgang Schulze,Boris Yu. Sternin Pdf

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

Author : Heinz O. Cordes,Bernhard Gramsch,Harold Widom
Publisher : Springer
Page : 495 pages
File Size : 42,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540478867

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Pseudo-Differential Operators by Heinz O. Cordes,Bernhard Gramsch,Harold Widom Pdf

Author : Luigi Rodino
Publisher : Springer Science & Business Media
Page : 449 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401156264

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Microlocal Analysis and Spectral Theory by Luigi Rodino Pdf

The NATO Advanced Study Institute "Microlocal Analysis and Spectral The ory" was held in Tuscany (Italy) at Castelvecchio Pascoli, in the district of Lucca, hosted by the international vacation center "11 Ciocco" , from September 23 to October 3, 1996. The Institute recorded the considerable progress realized recently in the field of Microlocal Analysis. In a broad sense, Microlocal Analysis is the modern version of the classical Fourier technique in solving partial differential equa tions, where now the localization proceeding takes place with respect to the dual variables too. Precisely, through the tools of pseudo-differential operators, wave-front sets and Fourier integral operators, the general theory of the lin ear partial differential equations is now reaching a mature form, in the frame of Schwartz distributions or other generalized functions. At the same time, Microlocal Analysis has grown up into a definite and independent part of Math ematical Analysis, with other applications all around Mathematics and Physics, one major theme being Spectral Theory for Schrodinger equation in Quantum Mechanics.

Author : Heinz Otto Cordes
Publisher : Cambridge University Press
Page : 398 pages
File Size : 41,7 Mb
Release : 1995-02-23
Category : Mathematics
ISBN : 9780521378642

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The Technique of Pseudodifferential Operators by Heinz Otto Cordes Pdf

Pseudodifferential operators arise naturally in a solution of boundary problems for partial differential equations. The formalism of these operators serves to make the Fourier-Laplace method applicable for nonconstant coefficient equations. This book presents the technique of pseudodifferential operators and its applications, especially to the Dirac theory of quantum mechanics. The treatment uses 'Leibniz formulas' with integral remainders or as asymptotic series. While a pseudodifferential operator is commonly defined by an integral formula, it also may be described by invariance under action of a Lie group. The author discusses connections to the theory of C*-algebras, invariant algebras of pseudodifferential operators under hyperbolic evolution, and the relation of the hyperbolic theory to the propagation of maximal ideals. The Technique of Pseudodifferential Operators will be of particular interest to researchers in partial differential equations and mathematical physics.