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Operators Of Class C 0 With Spectra In Multiply Connected Regions
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Book Synopsis Operators of Class C_0 with Spectra in Multiply Connected Regions by : Adele Zucchi
Download or read book Operators of Class C_0 with Spectra in Multiply Connected Regions written by Adele Zucchi and published by American Mathematical Soc.. This book was released on 1997 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let $\Omega$ be a bounded finitely connected region in the complex plane, whose boundary $\Gamma$ consists of disjoint, analytic, simple closed curves. The author 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, the author defines a weak$^*$-continuous functional calculus representation on the Banach algebra of bounded analytic functions on $\Omega$. An operator is said to be of class $C_0$ if the associated functional calculus has a non-trivial kernel. In this work, the author studies operators of class $C_0$, providing a complete classification into quasisimilarity classes, which is analogous to the case of the unit disk.
Book Synopsis Operators of Class C0 with Spectra in Multiply Connected Regions by : Adele Zucchi
Download or read book Operators of Class C0 with Spectra in Multiply Connected Regions written by Adele Zucchi and published by American Mathematical Soc.. This book was released on 1997-01-01 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: Just list for NBB purposes.
Book Synopsis Harmonic Analysis of Operators on Hilbert Space by : Béla Sz Nagy
Download or read book Harmonic Analysis of Operators on Hilbert Space written by Béla Sz Nagy and published by Springer Science & Business Media. This book was released on 2010-09-01 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the progress done in this direction in 1950-70. Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory. This second edition, in addition to revising and amending the original text, focuses on further developments of the theory, including the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective. For both of these classes, a wealth of material on structure, classification and invariant subspaces is included in Chapters IX and X. Several chapters conclude with a sketch of other developments related with (and developing) the material of the first edition.
Book Synopsis Invariants Under Tori of Rings of Differential Operators and Related Topics by : Ian Malcolm Musson
Download or read book Invariants Under Tori of Rings of Differential Operators and Related Topics written by Ian Malcolm Musson and published by American Mathematical Soc.. This book was released on 1998 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: If $G$ is a reductive algebraic group acting rationally on a smooth affine variety $X$, then it is generally believed that $D(X)^G$ has properties very similar to those of enveloping algebras of semisimple Lie algebras. In this book, the authors show that this is indeed the case when $G$ is a torus and $X=k^r\times (k^*)^s$. They give a precise description of the primitive ideals in $D(X)^G$ and study in detail the ring theoretical and homological properties of the minimal primitive quotients of $D(X)^G$. The latter are of the form $B^x=D(X)^G/({\mathfrak g}-\chi({\mathfrak g}))$ where ${\mathfrak g}=\textnormal{Lie}(G)$, $\chi\in {\mathfrak g}^\ast$ and ${\mathfrak g}-\chi({\mathfrak g})$ is the set of all $v-\chi(v)$ with $v\in {\mathfrak g}$. They occur as rings of twisted differential operators on toric varieties. It is also proven that if $G$ is a torus acting rationally on a smooth affine variety, then $D(X[LAMBDA]!/G)$ is a simple ring.
Book Synopsis Spectral Asymptotics on Degenerating Hyperbolic 3-Manifolds by : Józef Dodziuk
Download or read book Spectral Asymptotics on Degenerating Hyperbolic 3-Manifolds written by Józef Dodziuk and published by American Mathematical Soc.. This book was released on 1998 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the authors study asymptotics of the geometry and spectral theory of degenerating sequences of finite volume hyperbolic manifolds of three dimensions. Thurston's hyperbolic surgery theorem assets the existence of non-trivial sequences of finite volume hyperbolic three manifolds which converge to a three manifold with additional cusps. In the geometric aspect of their study, the authors use the convergence of hyperbolic metrics on the thick parts of the manifolds under consideration to investigate convergentce of tubes in the manifolds of the sequence to cusps of the limiting manifold. In the specral theory aspect of the work, they prove convergence of heat kernels. They then define a regualrized heat race associated to any finite volume, complete, hyperbolic three manifold, and study its asymptotic behaviour through degeneration. As an application of the analysis of the regularized heat trace, they study asymptotic behaviours of the spectral zeta function, determinant of the Laplacian, Selberg zeta function, and spectral counting functions through degeneration. The authors' methods are an adaptation to three dimensions of the earlier work of Jorgenson and Lundelius who investigated the asymptotic behaviour of spectral functions on degenerating families of finite area hyperbolic Riemann surfaces.
Book Synopsis Bosonic Construction of Vertex Operator Para-Algebras from Symplectic Affine Kac-Moody Algebras by : Michael David Weiner
Download or read book Bosonic Construction of Vertex Operator Para-Algebras from Symplectic Affine Kac-Moody Algebras written by Michael David Weiner and published by American Mathematical Soc.. This book was released on 1998 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: Begins with the bosonic construction of four level -1/2 irreducible representations of the symplectic affine Kac-Moody Lie algebra Cl. The direct sum of two of these is given the structure of a vertex operator algebra (VOA), and the direct sum of the other two is given the structure of a twisted VOA-module. The dissertation includes the bosonic analog of the fermionic construction of a vertex operator superalgebra from the four level 1 irreducible modules of type Dl. No index. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Existence and Persistence of Invariant Manifolds for Semiflows in Banach Space by : Peter W. Bates
Download or read book Existence and Persistence of Invariant Manifolds for Semiflows in Banach Space written by Peter W. Bates and published by American Mathematical Soc.. This book was released on 1998 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extends the theory for normally hyperbolic invariant manifolds to infinite dimensional dynamical systems in a Banach space, thereby providing tools for the study of PDE's and other infinite dimensional equations of evolution. In the process, the authors establish the existence of center-unstable and center-stable manifolds in a neighborhood of the unperturbed compact manifold. No index. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Controllability, Stabilization, and the Regulator Problem for Random Differential Systems by : Russell Johnson
Download or read book Controllability, Stabilization, and the Regulator Problem for Random Differential Systems written by Russell Johnson and published by American Mathematical Soc.. This book was released on 1998 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume develops a systematic study of time-dependent control processes. The basic problem of null controllability of linear systems is first considered. Using methods of ergodic theory and topological dynamics, general local null controllability criteria are given. Then the subtle question of global null controllability is studied. Next, the random linear feedback and stabilization problem is posed and solved. Using concepts of exponential dichotomy and rotation number for linear Hamiltonian systems, a solution of the Riccati equation is obtained which has extremely good robustness properties and which also preserves all the smoothness and recurrence properties of the coefficients. Finally, a general version of the local nonlinear feedback stabilization problem is solved.
Book Synopsis Annihilating Fields of Standard Modules of $\mathfrak {sl}(2, \mathbb {C})^\sim $ and Combinatorial Identities by : Arne Meurman
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 89 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 $\tilde{\mathfrak g}$, they construct the corresponding level $k$ vertex operator algebra and show that level $k$ highest weight $\tilde{\mathfrak g}$-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 $\tilde{\mathfrak g}$-module--the set of relations that defines standard modules. In the case when $\tilde{\mathfrak g}$ 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.
Book Synopsis Flat Extensions of Positive Moment Matrices: Recursively Generated Relations by : Raúl E. Curto
Download or read book Flat Extensions of Positive Moment Matrices: Recursively Generated Relations written by Raúl E. Curto and published by American Mathematical Soc.. This book was released on 1998 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the authors develop new computational tests for existence and uniqueness of representing measures $\mu$ in the Truncated Complex Moment Problem: $\gamma {ij}=\int \bar zizj\, d\mu$ $(0\le i+j\le 2n)$. Conditions for the existence of finitely atomic representing measures are expressed in terms of positivity and extension properties of the moment matrix $M(n)(\gamma )$ associated with $\gamma \equiv \gamma {(2n)}$: $\gamma {00}, \dots ,\gamma {0,2n},\dots ,\gamma {2n,0}$, $\gamma {00}>0$. This study includes new conditions for flat (i.e., rank-preserving) extensions $M(n+1)$ of $M(n)\ge 0$; each such extension corresponds to a distinct rank $M(n)$-atomic representing measure, and each such measure is minimal among representing measures in terms of the cardinality of its support. For a natural class of moment matrices satisfying the tests of recursive generation, recursive consistency, and normal consistency, the existence problem for minimal representing measures is reduced to the solubility of small systems of multivariable algebraic equations. In a variety of applications, including cases of the quartic moment problem ($n=2$), the text includes explicit contructions of minimal representing measures via the theory of flat extensions. Additional computational texts are used to prove non-existence of representing measures or the non-existence of minimal representing measures. These tests are used to illustrate, in very concrete terms, new phenomena, associated with higher-dimensional moment problems that do not appear in the classical one-dimensional moment problem.
Book Synopsis Wandering Vectors for Unitary Systems and Orthogonal Wavelets by : Xingde Dai
Download or read book Wandering Vectors for Unitary Systems and Orthogonal Wavelets written by Xingde Dai and published by American Mathematical Soc.. This book was released on 1998 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Investigates topological and structural properties of the set W(U) of all complete wandering vectors for a system U of unitary operators acting on a Hilbert space. The authors parameterize W(U) in terms of a fixed vector y and the set of all unitary operators which locally commute with U at y. No index. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies by : Wolfgang Bulla
Download or read book Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies written by Wolfgang Bulla and published by American Mathematical Soc.. This book was released on 1998 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work, the authors provide a self-contained discussion of all real-valued quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchies of completely integrable evolution equations. The approach utilizes algebro-geometric methods, factorization techniques for finite difference expressions, as well as Miura-type transformations. Detailed spectral theoretic properties of Lax pairs and theta function representations of the solutions are derived. Features: Simple and unified treatment of the topic. Self-contained development. Novel results for the Kac-van Moerbeke hierarchy and its algebro-geometric solutions.
Book Synopsis Almost Automorphic and Almost Periodic Dynamics in Skew-Product Semiflows by : Wenxian Shen
Download or read book Almost Automorphic and Almost Periodic Dynamics in Skew-Product Semiflows written by Wenxian Shen and published by American Mathematical Soc.. This book was released on 1998 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to the study of almost automorphic dynamics in differential equations. By making use of techniques from abstract topological dynamics, it is shown that almost automorphy, a notion which was introduced by S. Bochner in 1955, is essential and fundamental in the qualitative study of almost periodic differential equations.
Book Synopsis Rank 3 Amalgams by : Bernd Stellmacher
Download or read book Rank 3 Amalgams written by Bernd Stellmacher and published by American Mathematical Soc.. This book was released on 1998 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians working in classical linear algebraic
Book Synopsis Hopf Algebras, Polynomial Formal Groups, and Raynaud Orders by : Lindsay Childs
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 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book 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.
Book Synopsis Differential Equations Methods for the Monge-Kantorovich Mass Transfer Problem by : Lawrence C. Evans
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 66 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 $- \mathrm{div}(\vert DU_p\vert^{p-2}Du_p)=f^+-f^-$ in the limit as $p\rightarrow\infty$. The idea is to show $u_p\rightarrow u$, where $u$ satisfies $\vert Du\vert\leq 1,-\mathrm{div}(aDu)=f^+-f^-$ for some density $a\geq0$, and then to build a flow by solving a nonautonomous ODE involving $a, Du, f^+$ and $f^-$.
Book Synopsis Cutting Brownian Paths by : Richard F. Bass
Download or read book Cutting Brownian Paths written by Richard F. Bass and published by American Mathematical Soc.. This book was released on 1999 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: A long open problem in probability theory has been the following: Can the graph of planar Brownian motion be split by a straight line? In this volume, the authors provide a solution, discuss related works, and present a number of open problems.
