Classical Function Theory Operator Dilation Theory And Machine Computation On Multiply Connected Domains

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Classical Function Theory, Operator Dilation Theory, and Machine Computation on Multiply-Connected Domains

Author : Jim Agler
Publisher : American Mathematical Soc.
ISBN 13 : 0821840460
Total Pages : 176 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Classical Function Theory, Operator Dilation Theory, and Machine Computation on Multiply-Connected Domains by : Jim Agler

Download or read book Classical Function Theory, Operator Dilation Theory, and Machine Computation on Multiply-Connected Domains written by Jim Agler and published by American Mathematical Soc.. This book was released on 2008 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work begins with the presentation of generalizations of the classical Herglotz Representation Theorem for holomorphic functions with positive real part on the unit disc to functions with positive real part defined on multiply-connected domains. The generalized Herglotz kernels that appear in these representation theorems are then exploited to evolve new conditions for spectral set and rational dilation conditions over multiply-connected domains. These conditions form the basis for the theoretical development of a computational procedure for probing a well-known unsolved problem in operator theory, the so called rational dilation conjecture. Arbitrary precision algorithms for computing the Herglotz kernels on circled domains are presented and analyzed. These algorithms permit an effective implementation of the computational procedure which results in a machine generated counterexample to the rational dilation conjecture.

Compactification of the Drinfeld Modular Surfaces

Author : Thomas Lehmkuhl
Publisher : American Mathematical Soc.
ISBN 13 : 0821842447
Total Pages : 113 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Compactification of the Drinfeld Modular Surfaces by : Thomas Lehmkuhl

Download or read book Compactification of the Drinfeld Modular Surfaces written by Thomas Lehmkuhl and published by American Mathematical Soc.. This book was released on 2009-01-21 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article the author describes in detail a compactification of the moduli schemes representing Drinfeld modules of rank 2 endowed with some level structure. The boundary is a union of copies of moduli schemes for Drinfeld modules of rank 1, and its points are interpreted as Tate data. The author also studies infinitesimal deformations of Drinfeld modules with level structure.

The Recognition Theorem for Graded Lie Algebras in Prime Characteristic

Author : Georgia Benkart
Publisher : American Mathematical Soc.
ISBN 13 : 0821842269
Total Pages : 164 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Recognition Theorem for Graded Lie Algebras in Prime Characteristic by : Georgia Benkart

Download or read book The Recognition Theorem for Graded Lie Algebras in Prime Characteristic written by Georgia Benkart and published by American Mathematical Soc.. This book was released on 2009 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Volume 197, number 920 (second of 5 numbers)."

Weakly Differentiable Mappings between Manifolds

Author : Piotr Hajłasz
Publisher : American Mathematical Soc.
ISBN 13 : 0821840797
Total Pages : 88 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Weakly Differentiable Mappings between Manifolds by : Piotr Hajłasz

Download or read book Weakly Differentiable Mappings between Manifolds written by Piotr Hajłasz and published by American Mathematical Soc.. This book was released on 2008 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study Sobolev classes of weakly differentiable mappings $f: {\mathbb X}\rightarrow {\mathbb Y}$ between compact Riemannian manifolds without boundary. These mappings need not be continuous. They actually possess less regularity than the mappings in ${\mathcal W}{1, n}({\mathbb X}\, \, {\mathbb Y})\, $, $n=\mbox{dim}\, {\mathbb X}$. The central themes being discussed a

Handbook of Linear Algebra, Second Edition

Author : Leslie Hogben
Publisher : CRC Press
ISBN 13 : 1466507284
Total Pages : 1906 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Handbook of Linear Algebra, Second Edition by : Leslie Hogben

Download or read book Handbook of Linear Algebra, Second Edition written by Leslie Hogben and published by CRC Press. This book was released on 2013-11-26 with total page 1906 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters. New to the Second Edition Separate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of matrices, generalized inverses, matrices over finite fields, invariant subspaces, representations of quivers, and spectral sets New chapters on combinatorial matrix theory topics, such as tournaments, the minimum rank problem, and spectral graph theory, as well as numerical linear algebra topics, including algorithms for structured matrix computations, stability of structured matrix computations, and nonlinear eigenvalue problems More chapters on applications of linear algebra, including epidemiology and quantum error correction New chapter on using the free and open source software system Sage for linear algebra Additional sections in the chapters on sign pattern matrices and applications to geometry Conjectures and open problems in most chapters on advanced topics Highly praised as a valuable resource for anyone who uses linear algebra, the first edition covered virtually all aspects of linear algebra and its applications. This edition continues to encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, and applications of linear algebra to various disciplines while also covering up-to-date software packages for linear algebra computations.

Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups

Author : John Rognes
Publisher : American Mathematical Soc.
ISBN 13 : 0821840762
Total Pages : 154 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups by : John Rognes

Download or read book Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups written by John Rognes and published by American Mathematical Soc.. This book was released on 2008 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author introduces the notion of a Galois extension of commutative $S$-algebras ($E_\infty$ ring spectra), often localized with respect to a fixed homology theory. There are numerous examples, including some involving Eilenberg-Mac Lane spectra of commutative rings, real and complex topological $K$-theory, Lubin-Tate spectra and cochain $S$-algebras. He establishes the main theorem of Galois theory in this generality. Its proof involves the notions of separable and etale extensions of commutative $S$-algebras, and the Goerss-Hopkins-Miller theory for $E_\infty$ mapping spaces. He shows that the global sphere spectrum $S$ is separably closed, using Minkowski's discriminant theorem, and he estimates the separable closure of its localization with respect to each of the Morava $K$-theories. He also defines Hopf-Galois extensions of commutative $S$-algebras and studies the complex cobordism spectrum $MU$ as a common integral model for all of the local Lubin-Tate Galois extensions. The author extends the duality theory for topological groups from the classical theory for compact Lie groups, via the topological study by J. R. Klein and the $p$-complete study for $p$-compact groups by T. Bauer, to a general duality theory for stably dualizable groups in the $E$-local stable homotopy category, for any spectrum $E$.

The Generalized Triangle Inequalities in Symmetric Spaces and Buildings with Applications to Algebra

Author : Michael Kapovich
Publisher : American Mathematical Soc.
ISBN 13 : 0821840541
Total Pages : 98 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Generalized Triangle Inequalities in Symmetric Spaces and Buildings with Applications to Algebra by : Michael Kapovich

Download or read book The Generalized Triangle Inequalities in Symmetric Spaces and Buildings with Applications to Algebra written by Michael Kapovich and published by American Mathematical Soc.. This book was released on 2008 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors apply their results on the geometry of polygons in infinitesimal symmetric spaces and symmetric spaces and buildings to four problems in algebraic group theory. Two of these problems are generalizations of the problems of finding the constraints on the eigenvalues (resp. singular values) of a sum (resp. product) when the eigenvalues (singular values) of each summand (factor) are fixed. The other two problems are related to the nonvanishing of the structure constants of the (spherical) Hecke and representation rings associated with a split reductive algebraic group over $\mathbb{Q}$ and its complex Langlands' dual. The authors give a new proof of the Saturation Conjecture for $GL(\ell)$ as a consequence of their solution of the corresponding saturation problem for the Hecke structure constants for all split reductive algebraic groups over $\mathbb{Q}$.

Limit Theorems of Polynomial Approximation with Exponential Weights

Author : Michael I. Ganzburg
Publisher : American Mathematical Soc.
ISBN 13 : 0821840630
Total Pages : 178 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Limit Theorems of Polynomial Approximation with Exponential Weights by : Michael I. Ganzburg

Download or read book Limit Theorems of Polynomial Approximation with Exponential Weights written by Michael I. Ganzburg and published by American Mathematical Soc.. This book was released on 2008 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author develops the limit relations between the errors of polynomial approximation in weighted metrics and apply them to various problems in approximation theory such as asymptotically best constants, convergence of polynomials, approximation of individual functions, and multidimensional limit theorems of polynomial approximation.

A Proof of Alon's Second Eigenvalue Conjecture and Related Problems

Author : Joel Friedman
Publisher : American Mathematical Soc.
ISBN 13 : 0821842803
Total Pages : 114 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis A Proof of Alon's Second Eigenvalue Conjecture and Related Problems by : Joel Friedman

Download or read book A Proof of Alon's Second Eigenvalue Conjecture and Related Problems written by Joel Friedman and published by American Mathematical Soc.. This book was released on 2008 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: A $d$-regular graph has largest or first (adjacency matrix) eigenvalue $\lambda_1=d$. Consider for an even $d\ge 4$, a random $d$-regular graph model formed from $d/2$ uniform, independent permutations on $\{1,\ldots,n\}$. The author shows that for any $\epsilon>0$ all eigenvalues aside from $\lambda_1=d$ are bounded by $2\sqrt{d-1}\;+\epsilon$ with probability $1-O(n^{-\tau})$, where $\tau=\lceil \bigl(\sqrt{d-1}\;+1\bigr)/2 \rceil-1$. He also shows that this probability is at most $1-c/n^{\tau'}$, for a constant $c$ and a $\tau'$ that is either $\tau$ or $\tau+1$ (``more often'' $\tau$ than $\tau+1$). He proves related theorems for other models of random graphs, including models with $d$ odd.

Torus Fibrations, Gerbes, and Duality

Author : Ron Donagi
Publisher : American Mathematical Soc.
ISBN 13 : 0821840924
Total Pages : 104 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Torus Fibrations, Gerbes, and Duality by : Ron Donagi

Download or read book Torus Fibrations, Gerbes, and Duality written by Ron Donagi and published by American Mathematical Soc.. This book was released on 2008 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let $X$ be a smooth elliptic fibration over a smooth base $B$. Under mild assumptions, the authors establish a Fourier-Mukai equivalence between the derived categories of two objects, each of which is an $\mathcal{O} DEGREES{\times}$ gerbe over a genus one fibration which is a twisted form

Rank One Higgs Bundles and Representations of Fundamental Groups of Riemann Surfaces

Author : William Mark Goldman
Publisher : American Mathematical Soc.
ISBN 13 : 082184136X
Total Pages : 86 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Rank One Higgs Bundles and Representations of Fundamental Groups of Riemann Surfaces by : William Mark Goldman

Download or read book Rank One Higgs Bundles and Representations of Fundamental Groups of Riemann Surfaces written by William Mark Goldman and published by American Mathematical Soc.. This book was released on 2008 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: This expository article details the theory of rank one Higgs bundles over a closed Riemann surface $X$ and their relation to representations of the fundamental group of $X$. The authors construct an equivalence between the deformation theories of flat connections and Higgs pairs. This provides an identification of moduli spaces arising in different contexts. The moduli spaces are real Lie groups. From each context arises a complex structure, and the different complex structures define a hyperkähler structure. The twistor space, real forms, and various group actions are computed explicitly in terms of the Jacobian of $X$. The authors describe the moduli spaces and their geometry in terms of the Riemann period matrix of $X$.

Complicial Sets Characterising the Simplicial Nerves of Strict $\omega $-Categories

$Download Complicial Sets Characterising the Simplicial Nerves of Strict $\omega $-Categories PDF Online Free$

Author : Dominic Verity
Publisher : American Mathematical Soc.
ISBN 13 : 0821841424
Total Pages : 208 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Complicial Sets Characterising the Simplicial Nerves of Strict $\omega $-Categories by : Dominic Verity

Download or read book Complicial Sets Characterising the Simplicial Nerves of Strict $\omega $-Categories written by Dominic Verity and published by American Mathematical Soc.. This book was released on 2008 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary purpose of this work is to characterise strict $\omega$-categories as simplicial sets with structure. The author proves the Street-Roberts conjecture in the form formulated by Ross Street in his work on Orientals, which states that they are exactly the ``complicial sets'' defined and named by John Roberts in his handwritten notes of that title (circa 1978). On the way the author substantially develops Roberts' theory of complicial sets itself and makes contributions to Street's theory of parity complexes. In particular, he studies a new monoidal closed structure on the category of complicial sets which he shows to be the appropriate generalisation of the (lax) Gray tensor product of 2-categories to this context. Under Street's $\omega$-categorical nerve construction, which the author shows to be an equivalence, this tensor product coincides with those of Steiner, Crans and others.

Representations of Shifted Yangians and Finite $W$-algebras

Author : Jonathan Brundan
Publisher : American Mathematical Soc.
ISBN 13 : 0821842161
Total Pages : 122 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Representations of Shifted Yangians and Finite $W$-algebras by : Jonathan Brundan

Download or read book Representations of Shifted Yangians and Finite $W$-algebras written by Jonathan Brundan and published by American Mathematical Soc.. This book was released on 2008 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study highest weight representations of shifted Yangians over an algebraically closed field of characteristic $0$. In particular, they classify the finite dimensional irreducible representations and explain how to compute their Gelfand-Tsetlin characters in terms of known characters of standard modules and certain Kazhdan-Lusztig polynomials. The authors' approach exploits the relationship between shifted Yangians and the finite W-algebras associated to nilpotent orbits in general linear Lie algebras.

The Stable Manifold Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential Equations

Author : Salah-Eldin Mohammed
Publisher : American Mathematical Soc.
ISBN 13 : 0821842501
Total Pages : 120 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Stable Manifold Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential Equations by : Salah-Eldin Mohammed

Download or read book The Stable Manifold Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential Equations written by Salah-Eldin Mohammed and published by American Mathematical Soc.. This book was released on 2008 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main objective of this paper is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations and stochastic partial differential equations near stationary solutions.

Bernoulli Free-Boundary Problems

Author : Eugene Shargorodsky
Publisher : American Mathematical Soc.
ISBN 13 : 0821841890
Total Pages : 86 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Bernoulli Free-Boundary Problems by : Eugene Shargorodsky

Download or read book Bernoulli Free-Boundary Problems written by Eugene Shargorodsky and published by American Mathematical Soc.. This book was released on 2008 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: Questions of existence, multiplicity, and regularity of free boundaries for prescribed data need to be addressed and their solutions lead to nonlinear problems. In this paper an equivalence is established between Bernoulli free-boundary problems and a class of equations for real-valued functions of one real variable.

Spinor Genera in Characteristic 2

Author : Yuanhua Wang
Publisher : American Mathematical Soc.
ISBN 13 : 0821841661
Total Pages : 104 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Spinor Genera in Characteristic 2 by : Yuanhua Wang

Download or read book Spinor Genera in Characteristic 2 written by Yuanhua Wang and published by American Mathematical Soc.. This book was released on 2008 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this paper is to establish the spinor genus theory of quadratic forms over global function fields in characteristic 2. The first part of the paper computes the integral spinor norms and relative spinor norms. The second part of the paper gives a complete answer to the integral representations of one quadratic form by another with more than four variables over a global function field in characteristic 2.

Toroidal Dehn Fillings on Hyperbolic 3-Manifolds

Author : Cameron Gordon
Publisher : American Mathematical Soc.
ISBN 13 : 082184167X
Total Pages : 154 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Toroidal Dehn Fillings on Hyperbolic 3-Manifolds by : Cameron Gordon

Download or read book Toroidal Dehn Fillings on Hyperbolic 3-Manifolds written by Cameron Gordon and published by American Mathematical Soc.. This book was released on 2008 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors determine all hyperbolic $3$-manifolds $M$ admitting two toroidal Dehn fillings at distance $4$ or $5$. They show that if $M$ is a hyperbolic $3$-manifold with a torus boundary component $T 0$, and $r,s$ are two slopes on $T 0$ with $\Delta(r,s) = 4$ or $5$ such that $M(r)$ and $M(s)$ both contain an essential torus, then $M$ is either one of $14$ specific manifolds $M i$, or obtained from $M 1, M 2, M 3$ or $M {14}$ by attaching a solid torus to $\partial M i - T 0$.All the manifolds $M i$ are hyperbolic, and the authors show that only the first three can be embedded into $S3$. As a consequence, this leads to a complete classification of all hyperbolic knots in $S3$ admitting two toroidal surgeries with distance at least $4$.