Elliptic operators and Lie groups

Author: Derek W. Robinson

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Mathematics

Page: 558

View: 339

Elliptic operators arise naturally in several different mathematical settings, notably in the representation theory of Lie groups, the study of evolution equations, and the examination of Riemannian manifolds. This book develops the basic theory of elliptic operators on Lie groups and thereby extends the conventional theory of parabolic evolution equations to a natural noncommutative context. In order to achieve this goal, the author presents a synthesis of ideas from partial differential equations, harmonic analysis, functional analysis, and the theory of Lie groups. He begins by discussing the abstract theory of general operators with complex coefficients before concentrating on the central case of second-order operators with real coefficients. A full discussion of second-order subelliptic operators is also given. Prerequisites are a familiarity with basic semigroup theory, the elementary theory of Lie groups, and a firm grounding in functional analysis as might be gained from the first year of a graduate course.
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Quantum and Non-Commutative Analysis

Past, Present and Future Perspectives

Author: Huzihiro Araki,Keiichi R. Ito,Akitaka Kishimoto,Izumi Ojima

Publisher: Springer Science & Business Media

ISBN: 9401728232

Category: Science

Page: 464

View: 7416

In the past decade, there has been a sudden and vigorous development in a number of research areas in mathematics and mathematical physics, such as theory of operator algebras, knot theory, theory of manifolds, infinite dimensional Lie algebras and quantum groups (as a new topics), etc. on the side of mathematics, quantum field theory and statistical mechanics on the side of mathematical physics. The new development is characterized by very strong relations and interactions between different research areas which were hitherto considered as remotely related. Focussing on these new developments in mathematical physics and theory of operator algebras, the International Oji Seminar on Quantum Analysis was held at the Kansai Seminar House, Kyoto, JAPAN during June 25-29, 1992 by a generous sponsorship of the Japan Society for the Promotion of Science and the Fujihara Foundation of Science, as a workshop of relatively small number of (about 50) invited participants. This was followed by an open Symposium at RIMS, described below by its organizer, A. Kishimoto. The Oji Seminar began with two key-note addresses, one by V.F.R. Jones on Spin Models in Knot Theory and von Neumann Algebras and by A. Jaffe on Where Quantum Field Theory Has Led. Subsequently topics such as Subfactors and Sector Theory, Solvable Models of Statistical Mechanics, Quantum Field Theory, Quantum Groups, and Renormalization Group Ap proach, are discussed. Towards the end, a panel discussion on Where Should Quantum Analysis Go? was held.
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Evolution Equations and Their Applications in Physical and Life Sciences

Author: G Lumer

Publisher: CRC Press

ISBN: 9780824790103

Category: Medical

Page: 530

View: 5857

This volume presents a collection of lectures on linear partial differntial equations and semigroups, nonlinear equations, stochastic evolutionary processes, and evolution problems from physics, engineering and mathematical biology. The contributions come from the 6th International Conference on Evolution Equations and Their Applications in Physical and Life Sciences, held in Bad Herrenalb, Germany.
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Algebraic Groups and Lie Groups

A Volume of Papers in Honour of the Late R. W. Richardson

Author: T. A. Springer,Roger Wolcott Richardson,G. I. Lehrer,Alan L. Carey,Michael Murray

Publisher: Cambridge University Press

ISBN: 9780521585323

Category: Mathematics

Page: 384

View: 8724

This volume is a unique and comprehensive collection of works by some of the world's leading researchers. Papers on algebraic geometry, algebraic groups, and Lie groups are woven together to form a connection between the study of symmetry and certain algebraic structures. This connection reflects the interests of R. W. Richardson who studied the links between representation theory and the structure and geometry of algebraic groups. In particular, the papers address Kazhdan-Lusztig theory, quantum groups, spherical varieties, symmetric varieties, cohomology of varieties, purity, Schubert geometry, invariant theory and symmetry breaking. For those working on algebraic and Lie groups, this book will be a wealth of fascinating material.
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Analysis on Lie Groups with Polynomial Growth

Author: Nick Dungey,A.F.M. ter Elst,Derek William Robinson

Publisher: Springer Science & Business Media

ISBN: 9780817632250

Category: Mathematics

Page: 312

View: 4040

Analysis on Lie Groups with Polynomial Growth is the first book to present a method for examining the surprising connection between invariant differential operators and almost periodic operators on a suitable nilpotent Lie group. It deals with the theory of second-order, right invariant, elliptic operators on a large class of manifolds: Lie groups with polynomial growth. In systematically developing the analytic and algebraic background on Lie groups with polynomial growth, it is possible to describe the large time behavior for the semigroup generated by a complex second-order operator with the aid of homogenization theory and to present an asymptotic expansion. Further, the text goes beyond the classical homogenization theory by converting an analytical problem into an algebraic one. This work is aimed at graduate students as well as researchers in the above areas. Prerequisites include knowledge of basic results from semigroup theory and Lie group theory.
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Report

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 3913

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Subject Guide to Books in Print

An Index to the Publishers' Trade List Annual

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 3882

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Quantum symmetries on operator algebras

Author: David E. Evans,Yasuyuki Kawahigashi

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Mathematics

Page: 829

View: 3432

In the last 20 years, the study of operator algebras has developed from a branch of functional analysis to a central field of mathematics with applications in both pure mathematics and mathematical physics. The theory was initiated by von Neumann and Murray as a tool for studying group representations and as a framework for quantum mechanics, and has since kept in touch with its roots in physics as a framework for quantum statistical mechanics and the formalism of algebraic quantum field theory. However, in 1981, the study of operator algebras took a new turn with the introduction by Vaughn Jones of subfactor theory, leading to remarkable connections with knot theory, 3-manifolds, quantum groups, and integrable systems in statistical mechanics and conformal field theory. This book, one of the first in the area, looks at these combinatorial-algebraic developments from the perspective of operator algebras. With minimal prerequisites from classical theory, it brings the reader to the forefront of research.
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General pattern theory

a mathematical study of regular structures

Author: Ulf Grenander

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Computers

Page: 899

View: 4995

The aim of pattern theory is to create mathematical knowledge representations of complex systems, analyze the mathematical properties of the resulting regular structures, and to apply them to practically occurring patterns in nature and the man-made world. Starting from an algebraic formulation of such representations they are studied in terms of their topological, dynamical and probabilistic aspects. Patterns are expressed through their typical behavior as well as through their variability around their typical form. Employing the representations (regular structures) algorithms are derived for the understanding, recognition, and restoration of observed patterns. The algorithms are investigated through computer experiments. The book is intended for statisticians and mathematicians with an interest in image analysis and pattern theory.
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