Principal Symbol Calculus on Contact Manifolds
Author | : Yuri Kordyukov |
Publisher | : Springer Nature |
Total Pages | : 167 |
Release | : |
Genre | : |
ISBN | : 3031699262 |
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Author | : Yuri Kordyukov |
Publisher | : Springer Nature |
Total Pages | : 167 |
Release | : |
Genre | : |
ISBN | : 3031699262 |
Author | : Michael Spivak |
Publisher | : Westview Press |
Total Pages | : 164 |
Release | : 1965 |
Genre | : Science |
ISBN | : 9780805390216 |
This book uses elementary versions of modern methods found in sophisticated mathematics to discuss portions of "advanced calculus" in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level.
Author | : Gerd Grubb |
Publisher | : American Mathematical Soc. |
Total Pages | : 338 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : 082183536X |
In recent years, increasingly complex methods have been brought into play in the treatment of geometric and topological problems for partial differential operators on manifolds. This collection of papers, resulting from a Workshop on Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds, provides a broad picture of these methods with new results. Subjects in the book cover a wide variety of topics, from recent advances in index theory and the more general boundary, to applications of those invariants in geometry, topology, and physics. Papers are grouped into four parts: Part I gives an overview of the subject from various points of view. Part II deals with spectral invariants, such as geometric and topological questions. Part IV deals specifically with problems on manifolds with singularities. The book is suitable for graduate students and researchers interested in spectral problems in geometry.
Author | : Raphael Ponge |
Publisher | : American Mathematical Soc. |
Total Pages | : 150 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 0821841483 |
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.
Author | : Anthony W. Knapp |
Publisher | : Springer Science & Business Media |
Total Pages | : 484 |
Release | : 2008-07-11 |
Genre | : Mathematics |
ISBN | : 0817644423 |
* Presents a comprehensive treatment with a global view of the subject * Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician
Author | : Steve Zelditch |
Publisher | : American Mathematical Soc. |
Total Pages | : 410 |
Release | : 2017-12-12 |
Genre | : Mathematics |
ISBN | : 1470410370 |
Eigenfunctions of the Laplacian of a Riemannian manifold can be described in terms of vibrating membranes as well as quantum energy eigenstates. This book is an introduction to both the local and global analysis of eigenfunctions. The local analysis of eigenfunctions pertains to the behavior of the eigenfunctions on wavelength scale balls. After re-scaling to a unit ball, the eigenfunctions resemble almost-harmonic functions. Global analysis refers to the use of wave equation methods to relate properties of eigenfunctions to properties of the geodesic flow. The emphasis is on the global methods and the use of Fourier integral operator methods to analyze norms and nodal sets of eigenfunctions. A somewhat unusual topic is the analytic continuation of eigenfunctions to Grauert tubes in the real analytic case, and the study of nodal sets in the complex domain. The book, which grew out of lectures given by the author at a CBMS conference in 2011, provides complete proofs of some model results, but more often it gives informal and intuitive explanations of proofs of fairly recent results. It conveys inter-related themes and results and offers an up-to-date comprehensive treatment of this important active area of research.
Author | : Loring W. Tu |
Publisher | : Springer Science & Business Media |
Total Pages | : 426 |
Release | : 2010-10-05 |
Genre | : Mathematics |
ISBN | : 1441974008 |
Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
Author | : James R. Munkres |
Publisher | : CRC Press |
Total Pages | : 296 |
Release | : 2018-02-19 |
Genre | : Mathematics |
ISBN | : 0429973772 |
A readable introduction to the subject of calculus on arbitrary surfaces or manifolds. Accessible to readers with knowledge of basic calculus and linear algebra. Sections include series of problems to reinforce concepts.
Author | : Richard Beals |
Publisher | : Princeton University Press |
Total Pages | : 212 |
Release | : 1988-08-21 |
Genre | : Business & Economics |
ISBN | : 9780691085012 |
The description for this book, Calculus on Heisenberg Manifolds. (AM-119), Volume 119, will be forthcoming.
Author | : Henri Moscovici |
Publisher | : American Mathematical Soc. |
Total Pages | : 337 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 0821849441 |
This volume represents the proceedings of the conference on Noncommutative Geometric Methods in Global Analysis, held in honor of Henri Moscovici, from June 29-July 4, 2009, in Bonn, Germany. Henri Moscovici has made a number of major contributions to noncommutative geometry, global analysis, and representation theory. This volume, which includes articles by some of the leading experts in these fields, provides a panoramic view of the interactions of noncommutative geometry with a variety of areas of mathematics. It focuses on geometry, analysis and topology of manifolds and singular spaces, index theory, group representation theory, connections of noncommutative geometry with number theory and arithmetic geometry, Hopf algebras and their cyclic cohomology.