Elliptic Theory On Singular Manifolds
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Elliptic Theory on Singular Manifolds
Author | : Vladimir E. Nazaikinskii,Anton Yu. Savin,Bert-Wolfgang Schulze,Boris Yu. Sternin |
Publsiher | : CRC Press |
Total Pages | : 372 |
Release | : 2005-08-12 |
Genre | : Mathematics |
ISBN | : 9781420034974 |
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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
Differential Equations on Singular Manifolds
Author | : Bert-Wolfgang Schulze,Boris Sternin,Viktor Evgenʹevich Shatalov |
Publsiher | : Wiley-VCH |
Total Pages | : 384 |
Release | : 1998 |
Genre | : Mathematics |
ISBN | : STANFORD:36105021928028 |
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In the book, new methods in the theory of differential equations on manifolds with singularities are presented. The semiclassical theory in quantum mechanics is employed, adapted to operators that are degenerate in a typical way. The degeneracies may be induced by singular geometries, e.g., conical or cuspidal ones. A large variety of non-standard degenerate operators are also discussed. The semiclassical approach yields new results and unexpected effects, also in classical situations. For instance, full asymptotic expansions for cuspidal singularities are constructed, and nonstationary problems on singular manifolds are treated. Moreover, finiteness theorems are obtained by using operator algebra methods in a unified framework. Finally the method of characteristics for general elliptic equations on manifolds with singularities is developed in the book.
Elliptic Mixed Transmission and Singular Crack Problems
Author | : Gohar Harutyunyan,Bert-Wolfgang Schulze |
Publsiher | : European Mathematical Society |
Total Pages | : 782 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 303719040X |
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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.
C algebras and Elliptic Theory II
Author | : Dan Burghelea,Richard Melrose,Alexander S. Mishchenko,Evgenij V. Troitsky |
Publsiher | : Springer Science & Business Media |
Total Pages | : 312 |
Release | : 2008-03-18 |
Genre | : Mathematics |
ISBN | : 9783764386047 |
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This book consists of a collection of original, refereed research and expository articles on elliptic aspects of geometric analysis on manifolds, including singular, foliated and non-commutative spaces. The topics covered include the index of operators, torsion invariants, K-theory of operator algebras and L2-invariants. There are contributions from leading specialists, and the book maintains a reasonable balance between research, expository and mixed papers.
Elliptic and Parabolic Equations
Author | : Joachim Escher,Elmar Schrohe,Jörg Seiler,Christoph Walker |
Publsiher | : Springer |
Total Pages | : 291 |
Release | : 2015-06-04 |
Genre | : Mathematics |
ISBN | : 9783319125473 |
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The international workshop on which this proceedings volume is based on brought together leading researchers in the field of elliptic and parabolic equations. Particular emphasis was put on the interaction between well-established scientists and emerging young mathematicians, as well as on exploring new connections between pure and applied mathematics. The volume contains material derived after the workshop taking up the impetus to continue collaboration and to incorporate additional new results and insights.
Pseudo differential Operators
Author | : Luigi Rodino,Bert-Wolfgang Schulze,Man Wah Wong |
Publsiher | : American Mathematical Soc. |
Total Pages | : 432 |
Release | : 2007-11-21 |
Genre | : Mathematics |
ISBN | : 0821871552 |
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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.
C algebras and Elliptic Theory
Author | : Bogdan Bojarski,Alexander S. Mishchenko,Evgenij V. Troitsky,Andrzej Weber |
Publsiher | : Springer Science & Business Media |
Total Pages | : 327 |
Release | : 2006-11-09 |
Genre | : Mathematics |
ISBN | : 9783764376871 |
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This book consists of reviewed original research papers and expository articles in index theory (especially on singular manifolds), topology of manifolds, operator and equivariant K-theory, Hopf cyclic cohomology, geometry of foliations, residue theory, Fredholm pairs and others, and applications in mathematical physics. The wide spectrum of subjects reflects the diverse directions of research for which the starting point was the Atiyah-Singer index theorem.
Transmutation Operators and Applications
Author | : Vladislav V. Kravchenko,Sergei M. Sitnik |
Publsiher | : Springer Nature |
Total Pages | : 685 |
Release | : 2020-04-11 |
Genre | : Mathematics |
ISBN | : 9783030359140 |
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Transmutation operators in differential equations and spectral theory can be used to reveal the relations between different problems, and often make it possible to transform difficult problems into easier ones. Accordingly, they represent an important mathematical tool in the theory of inverse and scattering problems, of ordinary and partial differential equations, integral transforms and equations, special functions, harmonic analysis, potential theory, and generalized analytic functions. This volume explores recent advances in the construction and applications of transmutation operators, while also sharing some interesting historical notes on the subject.