This book is devoted to explaining a wide range of applications of con- tinuous symmetry groups to physically important systems of differential equations.
In this presentation of the Galois correspondence, modem theories of groups and fields are used to study problems, some of which date back to the ancient Greeks.
Drawing on expertise from communication scholars who examine resilience within and across individual, relational, group/team, organizational, inter-organizational, and community levels, this handbook provides a wide-ranging resource for theory building, empirical investigations, and practical applications.
This volume is a consequence of a series of seminars presented by the authors at the Infrared Spectroscopy Institute, Canisius College, Buffalo, New York, over the last nine years.
This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincare upper half plane.
This second edition is fully updated, covering in particular new types of coherent states (the so-called Gazeau-Klauder coherent states, nonlinear coherent states, squeezed states, as used now routinely in quantum optics) and various generalizations of wavelets (wavelets on manifolds, curvelets, shearlets, etc.
Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians.
Asymptotic Geometric Analysis is concerned with the geometric and linear properties of finite dimensional objects, normed spaces, and convex bodies, especially with the asymptotics of their various quantitative parameters as the dimension tends to infinity.
Drinfeld Moduli Schemes and Automorphic Forms: The Theory of Elliptic Modules with Applications is based on the author's original work establishing the correspondence between ell-adic rank r Galois representations and automorphic representations of GL(r) over a function field, in the local case, and, in the global case, under a restriction at a single place.
Lectures on Finitely Generated Solvable Groups are based on the "e;Topics in Group Theory"e; course focused on finitely generated solvable groups that was given by Gilbert G.
This graduate textbook presents the basics of representation theory for finite groups from the point of view of semisimple algebras and modules over them.
This volume is the offspring of a week-long workshop on "e;Galois groups over Q and related topics,"e; which was held at the Mathematical Sciences Research Institute during the week March 23-27, 1987.
One of the pervasive phenomena in the history of science is the development of independent disciplines from the solution or attempted solutions of problems in other areas of science.
A companion volume to the text "e;Complex Variables: An Introduction"e; by the same authors, this book further develops the theory, continuing to emphasize the role that the Cauchy-Riemann equation plays in modern complex analysis.
The theory of algebraic groups results from the interaction of various basic techniques from field theory, multilinear algebra, commutative ring theory, algebraic geometry and general algebraic representation theory of groups and Lie algebras.
This volume is an outgrowth of the research project "e;The Inverse Ga- lois Problem and its Application to Number Theory"e; which was carried out in three academic years from 1999 to 2001 with the support of the Grant-in-Aid for Scientific Research (B) (1) No.
The analysis of orthogonal polynomials associated with general weights was a major theme in classical analysis in the twentieth century, and undoubtedly will continue to grow in importance in the future.
The aim of this book is to provide a systematic and practical account of methods of integration of ordinary and partial differential equations based on invariance under continuous (Lie) groups of trans- formations.
During the last ten years a powerful technique for the study of partial differential equations with regular singularities has developed using the theory of hyperfunctions.
Since its beginnings with Fourier (and as far back as the Babylonian astron- omers), harmonic analysis has been developed with the goal of unraveling the mysteries of the physical world of quasars, brain tumors, and so forth, as well as the mysteries of the nonphysical, but no less concrete, world of prime numbers, diophantine equations, and zeta functions.
