Series: Operator Theory: Advances and Applications , Preliminary entry 500
2009, Approx. 400 p., Hardcover
ISBN: 978-3-7643-8995-6
Due: April 2009
This cross-disciplinary volume brings together theoretical mathematicians, engineers and numerical analysts and publishes surveys and research articles related to the topics where Georg Heinig had made outstanding achievements. In particular, this includes contributions from the fields of structured matrices, fast algorithms, operator theory, and applications to system theory and signal processing.
Researchers in numerical analysis, matrix and operator theory, system theory and signal processing
Preface.- Recollections about Georg Heinig.- Research and survey articles.
Series: Operator Theory: Advances and Applications , Preliminary entry 900
2009, Approx. 350 p., Hardcover
ISBN: 978-3-7643-9897-2
Due: April 2009
The volume contains most of the invited lectures presented at the International Conference Analysis, PDEs and Applications, held in Rome in July 2008, and dedicated to Vladimir G. Maz'ya on the occasion of his 70th birthday.
The authors present surveys as well as new results in the areas in which V. G. Maz'ya gave seminal contributions.
Advanced students and researchers
Preface.- Surveys.- Research articles.
Series: Lecture Notes in Mathematics , Vol. 1970
2009, Approx. 355 p., Softcover
ISBN: 978-3-540-92795-2
Due: April 9, 2009
This volume presents a collection of courses introducing the reader to the recent progress with attention being paid to laying solid grounds and developing various basic tools.
An introductory chapter on lattice spin models is useful as a background for other lectures of the collection.
The topics include new results on phase transitions for gradient lattice models (with introduction to the techniques of the reflection positivity), stochastic geometry reformulation of classical and quantum Ising models, the localization/delocalization transition for directed polymers.
A general rigorous framework for theory of metastability is presented and particular applications in the context of Glauber and Kawasaki dynamics of lattice models are discussed.
A pedagogical account of several recently discussed topics in nonequilibrium statistical mechanics with an emphasis on general principles is followed by a discussion of kinetically constrained spin models that are reflecting important peculiar features of glassy dynamics.
Researchers and graduate students
Reflection Positivity and Phase Transitions in Lattice Spin Models.- Stochastic Geometry of Classical and Quantum Ising Models.- Localization Transition in Disordered Pinning Models.- Metastability.- Three Lectures on Metastability Under Stochastic Dynamics.- A Selection of Nonequilibrium Issues.- Facilitated Spin Models: Recent and new Results
Series: Lecture Notes in Mathematics,Vol. 1974
Subseries: Ecole d'Ete Probabilit.Saint-Flour
2009, Approx. 280 p., Softcover
ISBN: 978-3-642-00332-5
Due: April 16, 2009
Polymer chains that interact with themselves and/or with their environment are fascinating objects, displaying a range of interesting physical and chemical phenomena. The focus in this monograph is on the mathematical description of some of these phenomena, with particular emphasis on phase transitions as a function of interaction parameters, associated critical behavior and space-time scaling. Topics include: self-repellent polymers, self-attracting polymers, polymers interacting with interfaces, charged polymers, copolymers near linear or random selective interfaces, polymers interacting with random substrate and directed polymers in random environment. Different techniques are exposed, including the method of local times, large deviations, the lace expansion, generating functions, the method of excursions, ergodic theory, partial annealing estimates, coarse-graining techniques and martingales. Thus, this monograph offers a mathematical panorama of polymer chains, which even today holds plenty of challenges.
Researchers and graduate students
1 Introduction.- 2 Two Basic Models.- Part A Polymers with Self-Interaction. 3 Soft Polymers in Low Dimension.- 4 Soft Polymers in High Dimension.- 5 Elastic Polymers.- 6 Polymer Collapse.- 7 Polymer Adsorption.- Part B Polymers in Random Environment. 8 Charged Polymers.- 9 Copolymers near a Linear Selective Interface.- 10 Copolymers near a Random Selective Interface.- 11 Random Pinning and Wetting of Polymers.- 12 Polymers in a Random Potential.
Series: Pseudo-Differential Operators , Vol. 2
Approx. 650 p., 2009, Approx. 650 p., Softcover
ISBN: 978-3-7643-8513-2
Due: June 2009
This monograph develops a global quantization theory of pseudo-differential operators on compact Lie groups.
Traditionally, the theory of pseudo-differential operators was introduced in the Euclidean setting with the aim of tackling a number of important problems in analysis and in the theory of partial differential equations. This also yields a local theory of pseudo-differential operators on manifolds. The present book takes a different approach by using global symmetries of the space which are often available. First, a particular attention is paid to the theory of periodic operators, which are realized in the form of pseudo-differential and Fourier integral operators on the torus. Then, the cases of the unitary group SU(2) and the 3-sphere are analyzed in extensive detail. Finally, the monograph also develops elements of the theory of pseudo-differential operators on general compact Lie groups and homogeneous spaces.
The exposition of the book is self-contained and provides the reader with the background material surrounding the theory and needed for working with pseudo-differential operators in different settings. The background section of the book may be used for independent learning of different aspects of analysis and is complemented by numerous examples and exercises.
Advanced undergraduate students and researchers working in analysis, partial differential equations, geometry, algebra, applied mathematicians and engineers
2011, Approx. 400 p. 10 illus., Hardcover
ISBN: 978-0-387-09448-9
Due: October 2011
Builds on companion volume to cover the frontiers of current research by consistently placing emphasis on geometric considerations involving differential forms
Essentially self-contained, provides all necessary background, excepting modest prerequisites
Clear exposition includes careful explanations, illustrative examples, numerous exercises, and detailed cross-references to simplify a non-linear reading of the material
Symmetries play a decisive role in the natural sciences and throughout mathematics. Infinite-dimensional Lie theory deals with symmetries depending on infinitely many parameters. Infinite-dimensional Lie Groups provides a comprehensive introduction to this important subject by developing a global infinite-dimensional Lie theory on the basis that a Lie group is simply a manifold modeled on a locally convex space, equipped with a group structure with smooth group operations. The focus is on the local and global level, as well as on the translation mechanisms allowing or preventing passage between Lie groups and Lie algebras. Starting from scratch, the reader is led from the basics of the theory through to the frontiers of current research.
This second volume subtitled, Geometry and Topology, builds on its companion volume, General Theory and Main Examples, by consistently placing emphasis on geometric considerations involving differential forms of various types. This framework is applied to homotopy groups, extensions of Lie groups, integrability of infnite-dimensional Lie algebras, and relations to symplectic geometry. The aim is to lay the foundation for the development of a substantive body of literature addressing the global geometric perspective to compliment the abundance of existing Lie-algebraic results.
Together, these essentially self-contained texts provide all necessary background as regards generally locally convex spaces, finite-dimensional Lie theory and differential geometry, with its modest prerequisites limited to a basic knowledge of abstract algebra, point set topology, differentiable manifolds, and functional analysis in Banach spaces. The clear exposition includes careful explanations, illustrative examples, numerous exercises, and detailed cross-references to simplify a non-linear reading of the material.
Graduate students, researchers, mathematicians, Lie theorists, group theorists, math physicists
Preface from General Theory and Main Examples.- Preface.- Introduction.- Homotopy Groups of Infinite-dimensional Lie Groups.- Extensions of Lie Groups.- Integrability of Infinite-dimensional Lie Algebras.- Relations to Symplectic Geometry.- Weaker Lie Group Concepts.- Appendix A: Cohomology of Lie Algebras.- Appendix B: Locally Smooth Cohomology of Lie Groups.- Appendix C: Some Facts from K-theory.- Bibliography.- Index.- Set Index.