Harmonic Analysis and Special Functions on Symmetric Spaces (Perspectives in Mathematics)
by Gerrit Heckman
This text is derived from lecture notes for the European School of Group Theory, a forum providing high-level courses on recent developments in group theory. The topic is elaborated with statements of definitions and theorems; these in turn are augmented with examples. The authors extend the ideas of harmonic analysis on semisimple symmetric spaces to embrace the theory of hypergeometric and spherical functions to show that the K-variant Eisenstein integrals for G/H are hypergeometric functions...
Shapes and Diffeomorphisms (Applied Mathematical Sciences, #171)
by Laurent Younes
Shapes are complex objects to apprehend, as mathematical entities, in terms that also are suitable for computerized analysis and interpretation. This volume provides the background that is required for this purpose, including different approaches that can be used to model shapes, and algorithms that are available to analyze them. It explores, in particular, the interesting connections between shapes and the objects that naturally act on them, diffeomorphisms. The book is, as far as possible, sel...
Riemann Problems and Jupyter Solutions (Fundamentals of Algorithms)
by David I. Ketcheson, Randall J Leveque, and Mauricio J. del Razo
This book addresses an important class of mathematical problems (the Riemann problem) for first-order hyperbolic partial differential equations (PDEs), which arise when modeling wave propagation in applications such as fluid dynamics, traffic flow, acoustics, and elasticity. It covers the fundamental ideas related to classical Riemann solutions, including their special structure and the types of waves that arise, as well as the ideas behind fast approximate solvers for the Riemann problem. The...
This volume, first published in 2000, presents a classical approach to the foundations and development of the geometry of vector fields, describing vector fields in three-dimensional Euclidean space, triply-orthogonal systems and applications in mechanics. Topics covered include Pfaffian forms, systems in n-dimensional space, and foliations and their Godbillion-Vey invariant. There is much interest in the study of geometrical objects in n-dimensional Euclidean space and this volume provides a us...
Introduction to Symplectic Dirac Operators (Lecture Notes in Mathematics, #1887)
by Katharina Habermann and Lutz Habermann
This volume is the first one that gives a systematic and self-contained introduction to the theory of symplectic Dirac operators and reflects the current state of the subject. At the same time, it is intended to establish the idea that symplectic spin geometry and symplectic Dirac operators may give valuable tools in symplectic geometry and symplectic topology, which have become important fields and very active areas of mathematical research.
These twenty-six papers survey a cross section of current work in modern geometric measure theory and its applications in the calculus of variations. Presently the field consists of a jumble of new ideas, techniques and intuitive hunches; an exchange of information has been hindered, however, by the characteristic length and complexity of formal research papers in higher-dimensional geometric analysis. This volume provides an easier access to the material, including introductions and summaries o...
Geometric Integration Theory (Cornerstones)
by Steven G Krantz and Harold R. Parks
This textbook introduces geometric measure theory through the notion of currents. Currents, continuous linear functionals on spaces of differential forms, are a natural language in which to formulate types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Motivating key ideas with examples and figures, this book is a comprehensive introduction ideal for both self-study and for use in the cla...
Submanifolds in Carnot Groups (Publications of the Scuola Normale Superiore, #7)
by Davide Vittone
The book is devoted to the study of submanifolds in the setting of Carnot groups equipped with a sub-Riemannian structure; particular emphasis is given to the case of Heisenberg groups. A Geometric Measure Theory viewpoint is adopted, and features as intrinsic perimeters, Hausdorff measures, area formulae, calibrations and minimal surfaces are considered. Area formulae for the measure of submanifolds of arbitrary codimension are obtained in Carnot groups. Intrinsically regular hypersurfaces in t...
A Treatise on the Differential Geometry of Curves and Surfaces (1909)
by Luther Pfahler Eisenhart
Surface Area. (AM-35) (Annals of Mathematics Studies, #35)
by Lamberto Cesari
The description for this book, Surface Area. (AM-35), will be forthcoming.
Infinite Groups: Geometric, Combinatorial and Dynamical Aspects (Progress in Mathematics)
by L Bartholdi
Evolutionary Synthesis of Pattern Recognition Systems (Monographs in Computer Science) (Lecture Notes in Mathematics)
by Bir Bhanu, Krzysztof Krawiec, and Yingqiang Lin
Integrates computer vision, pattern recognition, and AI. Presents original research that will benefit researchers and professionals in computer vision, pattern recognition, target recognition, machine learning, evolutionary learning, image processing, knowledge discovery and data mining, cybernetics, robotics, automation and psychology
New Developments in Differential Geometry (Mathematics and Its Applications, #350)
In succession to our former meetings on differential geometry a Colloquium took place in Debrecen from July 26 to July 30, 1994. The Colloquium was organized by the University of Debrecen, the Debrecen Branch of the Hungarian Academy of Sciences and supported by the Janos Bolyai Mathematical Society. The Colloquium and especially this proceedings volume received an important financial contribution form OMFB in the framework of the ACCORD Programme no. H9112-0855. The Organizing Committee was the...
This book provides a complete exposition of equidistribution and counting problems weighted by a potential function of common perpendicular geodesics in negatively curved manifolds and simplicial trees. Avoiding any compactness assumptions, the authors extend the theory of Patterson-Sullivan, Bowen-Margulis and Oh-Shah (skinning) measures to CAT(-1) spaces with potentials. The work presents a proof for the equidistribution of equidistant hypersurfaces to Gibbs measures, and the equidistribution...
In this text, integral geometry deals with Radon's problem of representing a function on a manifold in terms of its integrals over certain submanifolds-hence the term the Radon transform. Examples and far-reaching generalizations lead to fundamental problems such as: (i) injectivity, (ii) inversion formulas, (iii) support questions, (iv) applications (e.g., to tomography, partial di erential equations and group representations). For the case of the plane, the inversion theorem and the support t...
Causal Symmetric Spaces (Perspectives in Mathematics)
by Gestur Olafsson, Joachim Hilgert, and Sigurdur Helgason
This text is intended to introduce researchers and graduate students with a solid background in Lie theory to the concepts of causal symmetric spaces. The authors intend also to make the basic results and their proofs available and to describe some important lines of research in the field. To date, results of recent studies considered "standard" by specialists have not been widely published. This book seeks to bring this information to students and researchers in geometry and analysis on causal...