Download or read book Model Theory and Linear Extreme Points in the Numerical Radius Unit Ball written by Michael A. Dritschel and published by American Mathematical Society(RI). This book was released on 2014-09-11 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir initiates a model theory-based study of the numerical radius norm. Guided by the abstract model theory of Jim Agler, the authors propose a decomposition for operators that is particularly useful in understanding their properties with respect to the numerical radius norm. Of the topics amenable to investigation with these tools, the following are presented: a complete description of the linear extreme points of the non-matrix (numerical radius) unit ball; several equivalent characterizations of matricial extremals in the unit ball, that is, those members which do not allow a nontrivial extension remaining in the unit ball; and applications to numerical ranges of matrices, including a complete parameterization of all matrices whose numerical ranges are closed disks.
Download or read book Model Theory and Linear Extreme Points in the Numerical Radius Unit Ball written by Michael A. Dritschel and published by American Mathematical Soc.. This book was released on 1997 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir initiates a model theory-based study of the numerical radius norm. Guided by the abstract model theory of Jim Agler, the authors propose a decomposition for operators that is particularly useful in understanding their properties with respect to the numerical radius norm. Of the topics amenable to investigation with these tools, the following are presented: a complete description of the linear extreme points of the non-matrix (numerical radius) unit ball; several equivalent characterizations of matricial extremals in the unit ball, that is, those members which do not allow a nontrivial extension remaining in the unit ball; and applications to numerical ranges of matrices, including a complete parameterization of all matrices whose numerical ranges are closed disks.
Download or read book Numerical Ranges of Hilbert Space Operators written by Hwa-Long Gau and published by Cambridge University Press. This book was released on 2021-08-05 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with elementary operator theory and matrix analysis, this book introduces the basic properties of the numerical range and gradually builds up the whole numerical range theory. Over 400 assorted problems, ranging from routine exercises to published research results, give you the chance to put the theory into practice and test your understanding. Interspersed throughout the text are numerous comments and references, allowing you to discover related developments and to pursue areas of interest in the literature. Also included is an appendix on basic convexity properties on the Euclidean space. Targeted at graduate students as well as researchers interested in functional analysis, this book provides a comprehensive coverage of classic and recent works on the numerical range theory. It serves as an accessible entry point into this lively and exciting research area.
Download or read book Gian Carlo Rota on Analysis and Probability written by Jean Dhombres and published by Springer Science & Business Media. This book was released on 2002-12-06 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gian-Carlo Rota was born in Vigevano, Italy, in 1932. He died in Cambridge, Mas sachusetts, in 1999. He had several careers, most notably as a mathematician, but also as a philosopher and a consultant to the United States government. His mathe matical career was equally varied. His early mathematical studies were at Princeton (1950 to 1953) and Yale (1953 to 1956). In 1956, he completed his doctoral thesis under the direction of Jacob T. Schwartz. This thesis was published as the pa per "Extension theory of differential operators I", the first paper reprinted in this volume. Rota's early work was in analysis, more specifically, in operator theory, differ ential equations, ergodic theory, and probability theory. In the 1960's, Rota was motivated by problems in fluctuation theory to study some operator identities of Glen Baxter (see [7]). Together with other problems in probability theory, this led Rota to study combinatorics. His series of papers, "On the foundations of combi natorial theory", led to a fundamental re-evaluation of the subject. Later, in the 1990's, Rota returned to some of the problems in analysis and probability theory which motivated his work in combinatorics. This was his intention all along, and his early death robbed mathematics of his unique perspective on linkages between the discrete and the continuous. Glimpses of his new research programs can be found in [2,3,6,9,10].
Download or read book Study of the Critical Points at Infinity Arising from the Failure of the Palais Smale Condition for n Body Type Problems written by Hasna Riahi and published by American Mathematical Soc.. This book was released on 1999 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work, the author examines the following: When the Hamiltonian system $m i \ddot{q} i + (\partial V/\partial q i) (t,q) =0$ with periodicity condition $q(t+T) = q(t),\; \forall t \in \germ R$ (where $q {i} \in \germ R{\ell}$, $\ell \ge 3$, $1 \le i \le n$, $q = (q {1},...,q {n})$ and $V = \sum V {ij}(t,q {i}-q {j})$ with $V {ij}(t,\xi)$ $T$-periodic in $t$ and singular in $\xi$ at $\xi = 0$) is posed as a variational problem, the corresponding functional does not satisfy the Palais-Smale condition and this leads to the notion of critical points at infinity. This volume is a study of these critical points at infinity and of the topology of their stable and unstable manifolds. The potential considered here satisfies the strong force hypothesis which eliminates collision orbits. The details are given for 4-body type problems then generalized to n-body type problems.
Download or read book Hodge Theory in the Sobolev Topology for the de Rham Complex written by Luigi Fontana and published by American Mathematical Soc.. This book was released on 1998 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the authors treat the full Hodge theory for the de Rham complex when calculated in the Sobolev topology rather than in the $L2$ topology. The use of the Sobolev topology strikingly alters the problem from the classical setup and gives rise to a new class of elliptic boundary value problems. The study takes place on both the upper half space and on a smoothly bounded domain. It features: a good introduction to elliptic theory, pseudo-differential operators, and boundary value problems; theorems completely explained and proved; and new geometric tools for differential analysis on domains and manifolds.
Download or read book Combinatorial Theory of the Free Product with Amalgamation and Operator Valued Free Probability Theory written by Roland Speicher and published by American Mathematical Soc.. This book was released on 1998 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: Free probability theory, introduced by Voiculescu, has developed very actively in the last few years and has had an increasing impact on quite different fields in mathematics and physics. Whereas the subject arose out of the field of von Neumann algebras, presented here is a quite different view of Voiculescu's amalgamated free product. This combinatorial description not only allows re-proving of most of Voiculescu's results in a concise and elegant way, but also opens the way for many new results. Unlike other approaches, this book emphasizes the combinatorial structure of the concept of ``freeness''. This gives an elegant and easily accessible description of freeness and leads to new results in unexpected directions. Specifically, a mathematical framework for otherwise quite ad hoc approximations in physics emerges.
Download or read book Differential Equations Methods for the Monge Kantorovich Mass Transfer Problem written by Lawrence C. Evans and published by American Mathematical Soc.. This book was released on 1999 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the authors demonstrate under some assumptions on $f $, $f $ that a solution to the classical Monge-Kantorovich problem of optimally rearranging the measure $\mu{ }=f dx$ onto $\mu =f dy$ can be constructed by studying the $p$-Laplacian equation $- \roman{div}(\vert DU_p\vert p-2}Du_p)=f -f $ in the limit as $p\rightarrow\infty$. The idea is to show $u_p\rightarrow u$, where $u$ satisfies $\vert Du\vert\leq 1, -\roman{div}(aDu)=f -f $ for some density $a\geq0$, and then to build a flow by solving a nonautonomous ODE involving $a, Du, f $ and $f $
Download or read book Annihilating Fields of Standard Modules of mathfrak sl 2 mathbb C sim and Combinatorial Identities written by Arne Meurman and published by American Mathematical Soc.. This book was released on 1999 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the authors show that a set of local admissible fields generates a vertex algebra. For an affine Lie algebra $\tilde{\frak g}$, they construct the corresponding level $k$ vertex operator algebra and show that level $k$ highest weight $\tilde{\frak g}$-modules are modules for this vertex operator algebra. They determine the set of annihilating fields of level $k$ standard modules and study the corresponding loop $\tilde{\frak g}$-module--the set of relations that defines standard modules. In the case when $\tilde{\frak g}$ is of type $A{(1)} 1$, they construct bases of standard modules parameterized by colored partitions, and as a consequence, obtain a series of Rogers-Ramanujan type combinatorial identities.
Download or read book Relations Related to Betweenness Their Structure and Automorphisms written by Samson Adepoju Adeleke and published by American Mathematical Soc.. This book was released on 1998 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is about tree-like structures, namely semilinear ordering, general betweenness relations, C-relations and D-relations. It contains a systematic study of betweenness and introduces C- and D- relations to describe the behaviour of points at infinity (leaves or ends or directions of trees). The focus is on structure theorems and on automorphism groups, with applications to the theory of infinite permutation groups.
Download or read book Hopf Algebras Polynomial Formal Groups and Raynaud Orders written by Lindsay Childs and published by American Mathematical Soc.. This book was released on 1998 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gives two new methods for constructing $p$-elementary Hopf algebra orders over the valuation ring $R$ of a local field $K$ containing the $p$-adic rational numbers. One method constructs Hopf orders using isogenies of commutative degree 2 polynomial formal groups of dimension $n$, and is built on a systematic study of such formal group laws. The other method uses an exponential generalization of a 1992 construction of Greither. Both constructions yield Raynaud orders as iterated extensions of rank $p$ Hopf algebras; the exponential method obtains all Raynaud orders whose invariants satisfy a certain $p$-adic condition.
Download or read book A Continuum Limit of the Toda Lattice written by Percy Deift and published by American Mathematical Soc.. This book was released on 1998 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the authors describe a continuum limit of the Toda ODE system, obtained by taking as initial data for the finite lattice successively finer discretizations of two smooth functions. Using the integrability of the finite Toda lattice, the authors adapt the method introduced by Lax and Levermore for the study of the small dispersion limit of the Korteweg de Vries equations to the case of the Toda lattice. A general class of initial data is considered which permits, in particular, the formation of shocks. A feature of the analysis in this book is an extensive use of techniques from the theory of Riemann-Hilbert problems.
Download or read book The Riemann Problem for the Transportation Equations in Gas Dynamics written by Wancheng Sheng and published by American Mathematical Soc.. This book was released on 1999 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the one-dimensional and two-dimensional Riemann problems for the transportation equations in gas dynamics are solved constructively. In either the 1-D or 2-D case, there are only two kinds of solutions: one involves Dirac delta waves, and the other involves vacuums, which has been merely discussed so far. The generalized Rankine-Hugoniot and entropy conditions for Dirac delta waves are clarified with viscous vanishing method. All of the existence, uniqueness and stability for viscous perturbations are proved analytically
Download or read book The Study of Minimax Inequalities and Applications to Economies and Variational Inequalities written by George Xian-Zhi Yuan and published by American Mathematical Soc.. This book was released on 1998 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unified treatment for the study of the existence of equilibria of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities, which strongly depend on his infinite dimensional version of the classical Knaster, Kuratowski and Mazurkiewicz Lemma (KKM Lemma) in 1961. Studied are applications of general system versions of minimax inequalities and generalized quasi-variational inequalities, and random abstract economies and its applications to the system of random quasi-variational inequalities are given.
Download or read book Abelian Galois Cohomology of Reductive Groups written by Mikhail Borovoi and published by American Mathematical Soc.. This book was released on 1998 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, a new function H 2/ab (K, G) of abelian Galois cohomology is introduced from the category of connected reductive groups G over a field K of characteristic 0 to the category of abelian groups. The abelian Galois cohomology and the abelianization map ab1: H1 (K, G) -- H 2/ab (K, G) are used to give a functorial, almost explicit description of the usual Galois cohomology set H1 (K, G) when K is a number field
Download or read book Morava K Theories and Localisation written by Mark Hovey and published by American Mathematical Soc.. This book was released on 1999 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians working in group theory and generalizations.
Download or read book Some Connections between Isoperimetric and Sobolev type Inequalities written by Serguei Germanovich Bobkov and published by American Mathematical Soc.. This book was released on 1997 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: For Borel probability measures on metric spaces, this text studies the interplay between isoperimetric and Sobolev-type inequalities. In particular the question of finding optimal constants via isoperimetric quantities is explored. Also given are necessary and sufficient conditions for the equivalence between the extremality of some sets in the isoperimetric problem and the validity of some analytic inequalities. The book devotes much attention to: the probability distributions on the real line; the normalized Lebesgue measure on the Euclidean sheres; and the canonical Gaussian measure on the Euclidean space.
