Linear algebra permeates mathematics, as well as physics and engineering. In this text for junior and senior undergraduates, Sadun treats diagonalization as a central tool in solving complicated problems in these subjects by reducing coupled linear…
The $3x 1$ problem, or Collatz problem, concerns the following seemingly innocent arithmetic procedure applied to integers: If an integer $x$ is odd then ""multiply by three and add one"", while if it is even then ""divide by two"". The $3x 1$ probl…
This book is written by award-winning author, Frank Morgan. It offers a simple and sophisticated point of view, reflecting Morgan's insightful teaching, lecturing, and writing style. Intended for undergraduates studying real analysis, this book buil…
The origins of the harmonic analysis go back to an ingenious idea of Fourier that any reasonable function can be represented as an infinite linear combination of sines and cosines. Today's harmonic analysis incorporates the elements of geometric mea…
This book is a collection of articles on abelian varieties and number theory dedicated to Gerhard Frey's 75th birthday. It contains original articles by experts in the area of arithmetic and algebraic geometry. The articles cover topics on Abelian v…
This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in tu…
Presents the story, part real, part fictional, of the exchanges between John Ball and Grigori Perelman. We are immersed in the tormented mind of a person who prefers the simple and secluded life to the prestige of his discoveries. We know the final…
This book is based on notes from a beginning graduate course on partial differential equations. Prerequisites for using the book are a solid undergraduate course in real analysis. There are more than 100 exercises in the book. Some of them are just…
The main object of this work is to present a powerful method of construction of subshifts which the authors use chiefly to construct WAP systems with various properties. Among many other applications of these so-called labeled subshifts, the authors…
Presents twenty papers on different aspects of modern analysis, including analytic and computational number theory, symbolic and numerical computation, theoretical and computational optimization, and development in nonsmooth and functional analysis…
Let G be a simple algebraic group defined over an algebraically closed field k whose characteristic is either 0 or a good prime for G, and let uEG be unipotent. The authors study the centralizer CG(u), especially its centre Z(CG(u)). They calculate…
This book presents, for the first time in English, the papers of Beltrami, Klein, and Poincare that brought hyperbolic geometry into the mainstream of mathematics. A recognition of Beltrami comparable to that given the pioneering works of Bolyai and…
Contains sections on Complex differential geometry, Partial differential equations, Homogeneous spaces, and Relativity.
Contains the author's Constructive Theory of Partitions, papers on Binary Matrices, and the lectures on the Theory of Reciprocants. This title provides an index and biographical notice of the author.
Covers group theory and its applications, plus the theory of algebraic numbers. This book includes such topics as algebraic functions, elliptic functions and class field theory.
Every eight years since 1961, the University of Georgia has hosted a major international topology conference aimed at disseminating important recent results and bringing together researchers at different stages of their careers. This volume contains…
This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame, Indiana. Presented are basic methods for obtaining various a priori estimates for second-order equations of elliptic type with par…
Measurement error models describe functional relationships among variables observed, subject to random errors of measurement. This book treats general aspects of the measurement problem and features a discussion of the history of measurement error m…
Concerned with the nonnegative solutions of $\Delta u = u^2$ in a bounded and smooth domain in $\mathbb{R}^d$, this title intends to prove that they are uniquely determined by their fine trace on the boundary as defined in [DK98a], answering a major…
This book studies the problem of the decomposition of a given random variable into a sum of independent random variables (components). Starting from the famous Cram\'er theorem, which says that all components of a normal random variable are also nor…
The main purpose of this paper is to prove the existence, and in some cases the uniqueness, of unitarily invariant measures on formal completions of groups associated to affine Kac-Moody algebras, and associated homogeneous spaces. The basic invaria…
Combinatorics is mathematics of enumeration, existence, construction, and optimization questions concerning finite sets. This text focuses on the first three types of questions and covers basic counting and existence principles, distributions, gener…
Considers linear bounded operators on a Hilbert space $H$ having $\overline \Omega$ as spectral set, and no normal summand with spectrum in $\gamma$. For each operator satisfying these properties, this work defines a weak$^*$-continuous functional c…
Translation of Vneshneiiaeiia geometrieiia vypuklykh poverkhnostei.
Covers the proceedings of the 1996 Rocky Mountain Mathematics Consortium conference on 'Composition Operators on Spaces of Analytic Functions' held at the University of Wyoming. This work features a collection of articles on composition operators in…
Contains lectures from the CBMS Regional Conference held at Harvey Mudd College, June 1977. This monograph consists of applications to nonlinear differential equations of the author's coincidental degree. It includes an bibliography covering many as…
This book is intended for graduate students and research mathematicians interested in operator theory, functional analysis, and vector lattices.
Explores the rich and complex structure of free lattices. This book presents an exposition of the basic theory of free lattices, projective lattices, and lattices which are bounded homomorphic images of a free lattice, as well as applications of the…
Collects articles that were presented at the DIMACS Workshop on Network Switching, held in July 1997 at Princeton University. This title includes papers that cover a variety of issues related to network switching, including network environment, rout…
This book is an introduction to the field of dynamical systems, in particular, to the special class of Hamiltonian systems. The authors aimed at keeping the requirements of mathematical techniques minimal but giving detailed proofs and many examples…
On the assumption that the $\Gamma$-orbits all have dimension equal to that of $\Gamma$, this title shows that there is a naturally defined $F$- and $\Gamma$-invariant measure $\nu$ of maximal entropy on $\Lambda$ (it is not assumed that the action…
Focuses primarily on topics in the area of the theory of functions of a complex variable.
Voiculescu's notion of asymptotic free independence is known for a large class of random matrices including independent unitary invariant matrices. This notion is extended for independent random matrices invariant in law by conjugation by permutatio…
Presents the theory of ordinary differential equations with constant coefficients. This work considers boundary value problems for ordinary equations, Green matrices, Green functions, the Lopatinskii condition, and Lyapunov stability. It also descri…
Addresses bicompact sets, the group of automorphisms of a homogeneous convex cone, Markov random sets, partial topological products, homology theory of polynomial ideals, Markov processes, and ring groups and the duality principle.
Includes papers on nonsmooth elliptic operators, vibro-stable differential equations, smooth ergodic flows on surfaces, projection spectra, and differential operators and their Fourier transforms.
Focuses on topics in algebra, including wreath products, group representations, dense extensions, nilpotency of ideals, and Kuros chains. This book also contains a chronology of the life of Aleksandr Gennadievic Kuros.
Covers complex homogeneous spaces, transformations of systems of boundary value problems, operations on the class of all groups, elliptic pseudodifferential operators, and analytical form of differential equations.
Includes topics such as associative hyper-envelopes of Lie algebras, an inverse problem of spectral analysis of ordinary differential equations, Cesaro means of Fourier series, open and near open mappings, finite ring groups, and the unimodular grou…
Includes papers on Lie groups, probabilistic number theory, transcendence, Dirichlet $L$-series, entire functions, spectral theory of differential equations, and variational problems.
Addresses Lie groups, complete spaces, the Cauchy problem for Laplace's equation, metric extensions, the Klein-Gordon equation, elliptic operators, and multiple repetitions of games.
Contains papers on such topics as several complex variables, algebraic functions, the power moment problem, quasilinear parabolic equations, trigonometric and orthogonal series, and modules from a categorical viewpoint.
Treats such topics as metric extensions, topological conjugacy, locally convex spaces, quotient measures, statistical physics, harmonic functions, and the Laplace-Levy operator.
Contains topics such as subdifferentials of convex functions, ergodictheorems for dynamical systems, noncommutative probability theory, limit density matrices, and conservative Hamiltonian systems.
Focuses on such areas as measure theory, scattering theory, statistical mechanics, ergodic theory, spectral analysis of operators, and category theory.
Covers factor representations of the anticommutation relations. This title also covers such topics as facial characteristics of convex sets, statistical physics, categories with involution, and many-valued mappings and Borel sets.
Presents modern algebra from first principles. This title combines standard materials and necessary algebraic manipulations with general concepts that clarify meaning and importance. It presents a conceptual approach to algebra that starts with a de…
Poncelet's theorem is a famous result in algebraic geometry, dating to the early part of the nineteenth century. It concerns closed polygons inscribed in one conic and circumscribed about another. The theorem is of great depth in that it relates to…
This volume contains the proceedings of three AMS Special Sessions on Computational Algebraic and Analytic Geometry for Low-Dimensional Varieties held January 8, 2007, in New Orleans, LA; January 6, 2009, in Washington, DC; and January 6, 2011, in N…
Defines the class of cycle-free partial orders (CFPOs), and analyzes the CFPOs fulfilling a natural transitivity assumption, called $k$-connected set transitivity ($k$-$CS$-transitivity). This work generalizes Droste's classification of the countabl…
Presents an introduction to the theory of quantum computing. This book starts with the basics of classical theory of computation: Turing machines, Boolean circuits, parallel algorithms, probabilistic computation, NP-complete problems, and the idea o…
