Parabolicity Volterra Calculus And Conical Singularities
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Parabolicity Volterra Calculus And Conical Singularities
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Author : Sergio Albeverio
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Parabolicity Volterra Calculus And Conical Singularities written by Sergio Albeverio and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Partial differential equations constitute an integral part of mathematics. They lie at the interface of areas as diverse as differential geometry, functional analysis, or the theory of Lie groups and have numerous applications in the applied sciences. A wealth of methods has been devised for their analysis. Over the past decades, operator algebras in connection with ideas and structures from geometry, topology, and theoretical physics have contributed a large variety of particularly useful tools. One typical example is the analysis on singular configurations, where elliptic equations have been studied successfully within the framework of operator algebras with symbolic structures adapted to the geometry of the underlying space. More recently, these techniques have proven to be useful also for studying parabolic and hyperbolic equations. Moreover, it turned out that many seemingly smooth, noncompact situations can be handled with the ideas from singular analysis. The three papers at the beginning of this volume highlight this aspect. They deal with parabolic equations, a topic relevant for many applications. The first article prepares the ground by presenting a calculus for pseudo differential operators with an anisotropic analytic parameter. In the subsequent paper, an algebra of Mellin operators on the infinite space-time cylinder is constructed. It is shown how timelike infinity can be treated as a conical singularity.
Parabolicity Volterra Calculus And Conical Singularities
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Author : Sergio Albeverio
language : en
Publisher:
Release Date : 2002-01
Parabolicity Volterra Calculus And Conical Singularities written by Sergio Albeverio and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01 with Mathematics categories.
Elliptic Mixed Transmission And Singular Crack Problems
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Author : Gohar Harutyunyan
language : en
Publisher: European Mathematical Society
Release Date : 2007
Elliptic Mixed Transmission And Singular Crack Problems written by Gohar Harutyunyan and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Mixed, transmission, or crack problems belong to the analysis of boundary value problems on manifolds with singularities. The Zaremba problem with a jump between Dirichlet and Neumann conditions along an interface on the boundary is a classical example. The central theme of this book is to study mixed problems in standard Sobolev spaces as well as in weighted edge spaces where the interfaces are interpreted as edges. Parametrices and regularity of solutions are obtained within a systematic calculus of boundary value problems on manifolds with conical or edge singularities. This calculus allows singularities on the interface and homotopies between mixed and crack problems. Additional edge conditions are computed in terms of relative index results. In a detailed final chapter, the intuitive ideas of the approach are illustrated, and there is a discussion of future challenges. A special feature of the text is the inclusion of many worked-out examples which help the reader to appreciate the scope of the theory and to treat new cases of practical interest. This book is addressed to mathematicians and physicists interested in models with singularities, associated boundary value problems, and their solvability strategies based on pseudo-differential operators. The material is also useful for students in higher semesters and young researchers, as well as for experienced specialists working in analysis on manifolds with geometric singularities, the applications of index theory and spectral theory, operator algebras with symbolic structures, quantisation, and asymptotic analysis.
Heisenberg Calculus And Spectral Theory Of Hypoelliptic Operators On Heisenberg Manifolds
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Author : Raphael Ponge
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Heisenberg Calculus And Spectral Theory Of Hypoelliptic Operators On Heisenberg Manifolds written by Raphael Ponge and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Calculus categories.
This memoir deals with the hypoelliptic calculus on Heisenberg manifolds, including CR and contact manifolds. In this context the main differential operators at stake include the Hormander's sum of squares, the Kohn Laplacian, the horizontal sublaplacian, the CR conformal operators of Gover-Graham and the contact Laplacian. These operators cannot be elliptic and the relevant pseudodifferential calculus to study them is provided by the Heisenberg calculus of Beals-Greiner andTaylor.
Pseudo Differential Operators
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Author : Luigi Rodino
language : en
Publisher: American Mathematical Soc.
Release Date : 2007-11-21
Pseudo Differential Operators written by Luigi Rodino and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-21 with Mathematics categories.
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.
Advances In Pseudo Differential Operators
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Author : Ryuichi Ashino
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Advances In Pseudo Differential Operators written by Ryuichi Ashino and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Crack Theory And Edge Singularities
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Author : D. V. Kapanadze
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Crack Theory And Edge Singularities written by D. V. Kapanadze and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
Boundary value problems for partial differential equations playa crucial role in many areas of physics and the applied sciences. Interesting phenomena are often connected with geometric singularities, for instance, in mechanics. Elliptic operators in corresponding models are then sin gular or degenerate in a typical way. The necessary structures for constructing solutions belong to a particularly beautiful and ambitious part of the analysis. Cracks in a medium are described by hypersurfaces with a boundary. Config urations of that kind belong to the category of spaces (manifolds) with geometric singularities, here with edges. In recent years the analysis on such (in general, stratified) spaces has become a mathematical structure theory with many deep relations with geometry, topology, and mathematical physics. Key words in this connection are operator algebras, index theory, quantisation, and asymptotic analysis. Motivated by Lame's system with two-sided boundary conditions on a crack we ask the structure of solutions in weighted edge Sobolov spaces and subspaces with discrete and continuous asymptotics. Answers are given for elliptic sys tems in general. We construct parametrices of corresponding edge boundary value problems and obtain elliptic regularity in the respective scales of weighted spaces. The original elliptic operators as well as their parametrices belong to a block matrix algebra of pseudo-differential edge problems with boundary and edge conditions, satisfying analogues of the Shapiro-Lopatinskij condition from standard boundary value problems. Operators are controlled by a hierarchy of principal symbols with interior, boundary, and edge components.
Geometric And Spectral Analysis
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Author : Pierre Albin
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-01
Geometric And Spectral Analysis written by Pierre Albin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-01 with Mathematics categories.
In 2012, the Centre de Recherches Mathématiques was at the center of many interesting developments in geometric and spectral analysis, with a thematic program on Geometric Analysis and Spectral Theory followed by a thematic year on Moduli Spaces, Extremality and Global Invariants. This volume contains original contributions as well as useful survey articles of recent developments by participants from three of the workshops organized during these programs: Geometry of Eigenvalues and Eigenfunctions, held from June 4-8, 2012; Manifolds of Metrics and Probabilistic Methods in Geometry and Analysis, held from July 2-6, 2012; and Spectral Invariants on Non-compact and Singular Spaces, held from July 23-27, 2012. The topics covered in this volume include Fourier integral operators, eigenfunctions, probability and analysis on singular spaces, complex geometry, Kähler-Einstein metrics, analytic torsion, and Strichartz estimates. This book is co-published with the Centre de Recherches Mathématiques.
Advances In Microlocal And Time Frequency Analysis
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Author : Paolo Boggiatto
language : en
Publisher: Springer Nature
Release Date : 2020-03-03
Advances In Microlocal And Time Frequency Analysis written by Paolo Boggiatto and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-03 with Mathematics categories.
The present volume gathers contributions to the conference Microlocal and Time-Frequency Analysis 2018 (MLTFA18), which was held at Torino University from the 2nd to the 6th of July 2018. The event was organized in honor of Professor Luigi Rodino on the occasion of his 70th birthday. The conference’s focus and the contents of the papers reflect Luigi’s various research interests in the course of his long and extremely prolific career at Torino University.
Pseudo Differential Operators Analysis Applications And Computations
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Author : Luigi Rodino
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-14
Pseudo Differential Operators Analysis Applications And Computations written by Luigi Rodino and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-14 with Mathematics categories.
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.