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New Publications Offered by The New Publications Offered by the AMS To subscribe to email notification of new AMS publications, please go to http://www.ams.org/bookstore-email. Algebra and Algebraic Introduction Geometry to Orthogonal, Symplectic and Unitary The Schrödinger Representations of Model for the Minimal Finite Groups Representation of the Carl R. Riehm, McMaster Indefinite Orthogonal University, Hamilton, ON, Group O(p; q) Canada, and The Fields Institute, Toronto, ON, Canada Toshiyuki Kobayashi, University of Tokyo, Japan, and Gen Mano, Orthogonal, symplectic and unitary representations of finite groups lie at the crossroads of two more traditional subjects of PricewaterhouseCoopers Aarata, mathematics—linear representations of finite groups, and the Tokyo, Japan theory of quadratic, skew symmetric and Hermitian forms—and thus inherit some of the characteristics of both. Contents: Introduction; Two models of the minimal representation of O(p; q); K-finite eigenvectors in the Schrödinger model L2(C); This book is written as an introduction to the subject and not as an Radial part of the inversion; Main theorem; Bessel distributions; encyclopaedic reference text. The principal goal is an exposition of Appendix: special functions; Bibliography; List of Symbols; Index. the known results on the equivalence theory, and related matters such as the Witt and Witt-Grothendieck groups, over the “classical” Memoirs of the American Mathematical Society, Volume 213, fields—algebraically closed, real closed, finite, local and global. A Number 1000 detailed exposition of the background material needed is given in August 2011, 132 pages, Softcover, ISBN: 978-0-8218-4757-2, the first chapter. 2010 Mathematics Subject Classification: 22E30; 22E46, 43A80, It was A. Fröhlich who first gave a systematic organization Individual member US$42.60, List US$71, Institutional member of this subject, in a series of papers beginning in 1969. His US$56.80, Order code MEMO/213/1000 paper Orthogonal and symplectic representations of groups represents the culmination of his published work on orthogonal and symplectic representations. The author has included most of the work from that paper, extending it to include unitary representations, and also providing new approaches, such as the use of the equivariant Brauer-Wall group in describing the principal invariants of orthogonal representations and their interplay with each other. This item will also be of interest to those working in number theory. Titles in this series are co-published with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada). Contents: Background material; Isometry representations of finite groups; Hermitian forms over semisimple algebras; Equivariant Witt-Grothendieck and Witt groups; Representations over finite, local and global fields; Fröhlich’s invariant, Clifford algebras and the equivariant Brauer-Wall group; Bibliography; Glossary; Index. August 2011 Notices of the AMS 1015 New Publications Offered by the AMS Fields Institute Monographs, Volume 28 Analysis August 2011, 291 pages, Hardcover, ISBN: 978-0-8218-4271-3, LC 2011017501, 2010 Mathematics Subject Classification: 20C15, 20C05, 11E81, 11E88, 16W22, AMS members US$79.20, List US$99, Order code FIM/28 Symmetries and Related Topics in Real Solutions to Differential and Equations from Difference Equations Geometry David Blázquez-Sanz, Frank Sottile, Texas A&M Universidad Sergio Arboleda, University, College Station, TX Bogatá, Colombia, Juan J. Morales-Ruiz, Technical Understanding, finding, or even deciding University of Madrid, Spain, and on the existence of real solutions to Jesús Rodríguez Lombardero, a system of equations is a difficult Universidad de Salamanca, Spain, problem with many applications outside of mathematics. While it is hopeless to Editors expect much in general, we know a surprising amount about these questions for systems which possess additional structure often This volume represents the 2009 Jairo Charris Seminar in coming from geometry. Symmetries of Differential and Difference Equations, which was held at the Universidad Sergio Arboleda in Bogotá, Colombia. This book focuses on equations from toric varieties and Grassmannians. Not only is much known about these, but such The papers include topics such as Lie symmetries, equivalence equations are common in applications. There are three main themes: transformations and differential invariants, group theoretical upper bounds on the number of real solutions, lower bounds on the methods in linear equations, namely differential Galois theory and number of real solutions, and geometric problems that can have Stokes phenomenon, and the development of some geometrical all solutions be real. The book begins with an overview, giving methods in theoretical physics. background on real solutions to univariate polynomials and the The reader will find new interesting results in symmetries of geometry of sparse polynomial systems. The first half of the book differential and difference equations, applications in classical and concludes with fewnomial upper bounds and with lower bounds to quantum mechanics, two fundamental problems of theoretical sparse polynomial systems. The second half of the book begins by mechanics, the mathematical nature of time in Lagrangian sampling some geometric problems for which all solutions can be mechanics and the preservation of the equations of motion by real, before devoting the last five chapters to the Shapiro Conjecture, changes of frame, and discrete Hamiltonian systems arising in in which the relevant polynomial systems have only real solutions. geometrical optics and analogous to those of finite quantum Contents: Overview; Real solutions of univariate polynomials; mechanics. Sparse polynomial systems; Toric degenerations and Kushnirenko’s This item will also be of interest to those working in mathematical theorem; Fewnomial upper bounds; Fewnomial upper bounds from physics. Gale dual polynomial systems; Lower bounds for sparse polynomial Contents: A. A. Monforte and J.-A. Weil, A reduction method systems; Some lower bounds for systems of polynomials; for higher order variational equations of Hamiltonian systems; Enumerative real algebraic geometry; The Shapiro Conjecture for N. H. Ibragimov, A survey on integration of parabolic equations Grassmannians; The Shapiro Conjecture for rational functions; by reducing them to the heat equation; S. Jiménez, Weil jets, Lie Proof of the Shapiro Conjecture for Grassmannians; Beyond the correspondences and applications; J. Mozo-Fernández, Some Shapiro Conjecture for the Grassmannian; The Shapiro Conjecture applications of summability: An illustrated survey; J. M. Díaz, The beyond the Grassmannian; Bibliography; Index of notation; Index. structure of time and inertial forces in Lagrangian mechanics; University Lecture Series, Volume 57 P J. Olver, Differential invariant algebras; J. Sauloy, The Stokes phenomenon for linear q-difference equations; K. B. Wolf, Finite September 2011, approximately 199 pages, Softcover, ISBN: 978- Hamiltonian systems on phase space. 0-8218-5331-3, 2010 Mathematics Subject Classification: 14P99; 14M25, 14M15, 14N15, 14P25, 12D10, AMS members US$37.60, Contemporary Mathematics, Volume 549 List US$47, Order code ULECT/57 September 2011, 165 pages, Softcover, ISBN: 978-0-8218-6872-0, LC 2011012079, 2010 Mathematics Subject Classification: 35A30, 34M15, 17B45, 35C05, 70A05, 37J05, 22F05, 53A04, 39A13, AMS members US$55.20, List US$69, Order code CONM/549 1016 Notices of the AMS Volume 58, Number 7 New Publications Offered by the AMS Noncommutative Function Spaces in Geometry and Global Modern Analysis Analysis Krzysztof Jarosz, Southern Alain Connes, College de Illinois University at Edwardsville, France, Paris, France, Alexander IL, Editor Gorokhovsky, University This volume contains the proceedings of Colorado, Boulder, CO, of the Sixth Conference on Function Matthias Lesch, Universität Spaces, which was held from May 18–22, Bonn, Germany, Markus Pflaum, 2010, at Southern Illinois University at University of Colorado, Boulder, Edwardsville. CO, and Bahram Rangipour, The papers cover a broad range of topics, including spaces and University of New Brunswick, algebras of analytic functions of one and of many variables (and operators on such spaces), spaces of integrable functions, spaces of Fredericton, NB, Canada, Editors Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects. This volume represents the proceedings of the conference on Noncommutative Geometric Methods in Global Analysis, held in Contents: A. V. Abanin, R. Ishimura, and L. H. Khoi, honor of Henri Moscovici, from June 29–July 4, 2009, in Bonn, Exponential-polynomial bases for null spaces of convolution −∞ Germany. operators in A ; M. Abel, Locally m-pseudoconvex algebras; N. Arcozzi, R. Rochberg, E. Sawyer, and B. D. Wick, Distance Henri Moscovici has made a number of major contributions to functions for reproducing kernel Hilbert spaces; H. A. Peimbert noncommutative geometry, global analysis, and representation and A. G. García, Some properties of families of functions in theory. This volume, which includes articles by some of the Cb(X; C), β); R. M. Aron and P. Rueda, p-compact homogeneous leading experts in these fields, provides a panoramic view of the polynomials from an ideal point of view; F. Botelho and J. Jamison, interactions of noncommutative geometry with a variety of areas of Homomorphisms of non-commutative Banach *-algebras of mathematics. It focuses on geometry,
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