Operators Of Class C 0 With Spectra In Multiply Connected Regions

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Operators of Class C_0 with Spectra in Multiply Connected Regions

Adele Zucchi
Operators of Class C 0 with Spectra in Multiply Connected Regions Book PDF

Author : Adele Zucchi
Publisher : American Mathematical Soc.
Page : 52 pages
File Size : 40,8 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821806265

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Operators of Class C_0 with Spectra in Multiply Connected Regions by Adele Zucchi Pdf

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.

Harmonic Analysis of Operators on Hilbert Space

Béla Sz Nagy,Ciprian Foias,Hari Bercovici,László Kérchy
Harmonic Analysis of Operators on Hilbert Space Book PDF

Author : Béla Sz Nagy,Ciprian Foias,Hari Bercovici,László Kérchy
Publisher : Springer Science & Business Media
Page : 481 pages
File Size : 48,6 Mb
Release : 2010-09-01
Category : Mathematics
ISBN : 9781441960931

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Harmonic Analysis of Operators on Hilbert Space by Béla Sz Nagy,Ciprian Foias,Hari Bercovici,László Kérchy Pdf

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.

Invariants Under Tori of Rings of Differential Operators and Related Topics

Ian Malcolm Musson,M. van den Bergh
Invariants Under Tori of Rings of Differential Operators and Related Topics Book PDF

Author : Ian Malcolm Musson,M. van den Bergh
Publisher : American Mathematical Soc.
Page : 100 pages
File Size : 52,9 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821808856

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Invariants Under Tori of Rings of Differential Operators and Related Topics by Ian Malcolm Musson,M. van den Bergh Pdf

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.

Bosonic Construction of Vertex Operator Para-Algebras from Symplectic Affine Kac-Moody Algebras

Michael David Weiner
Bosonic Construction of Vertex Operator Para Algebras from Symplectic Affine Kac Moody Algebras Book PDF

Author : Michael David Weiner
Publisher : American Mathematical Soc.
Page : 121 pages
File Size : 40,7 Mb
Release : 1998
Category : Kac-Moody algebras
ISBN : 9780821808665

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Bosonic Construction of Vertex Operator Para-Algebras from Symplectic Affine Kac-Moody Algebras by Michael David Weiner Pdf

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

Existence and Persistence of Invariant Manifolds for Semiflows in Banach Space

Peter W. Bates,Kening Lu,Chongchun Zeng
Existence and Persistence of Invariant Manifolds for Semiflows in Banach Space Book PDF

Author : Peter W. Bates,Kening Lu,Chongchun Zeng
Publisher : American Mathematical Soc.
Page : 145 pages
File Size : 44,7 Mb
Release : 1998
Category : Differentiable dynamical systems
ISBN : 9780821808689

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Existence and Persistence of Invariant Manifolds for Semiflows in Banach Space by Peter W. Bates,Kening Lu,Chongchun Zeng Pdf

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

Spectral Asymptotics on Degenerating Hyperbolic 3-Manifolds

Józef Dodziuk,Jay Jorgenson
Spectral Asymptotics on Degenerating Hyperbolic 3 Manifolds Book PDF

Author : Józef Dodziuk,Jay Jorgenson
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 45,7 Mb
Release : 1998
Category : Asymptotic expansions
ISBN : 9780821808375

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Spectral Asymptotics on Degenerating Hyperbolic 3-Manifolds by Józef Dodziuk,Jay Jorgenson Pdf

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.

Controllability, Stabilization, and the Regulator Problem for Random Differential Systems

Russell Johnson,Mahesh G. Nerurkar
Controllability Stabilization and the Regulator Problem for Random Differential Systems Book PDF

Author : Russell Johnson,Mahesh G. Nerurkar
Publisher : American Mathematical Soc.
Page : 63 pages
File Size : 54,7 Mb
Release : 1998
Category : Control theory
ISBN : 9780821808658

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Controllability, Stabilization, and the Regulator Problem for Random Differential Systems by Russell Johnson,Mahesh G. Nerurkar Pdf

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.

Annihilating Fields of Standard Modules of $\mathfrak {sl}(2, \mathbb {C})^\sim $ and Combinatorial Identities

Arne Meurman,Mirko Primc
Annihilating Fields of Standard Modules of mathfrak sl 2 mathbb C sim and Combinatorial Identities Book PDF

Author : Arne Meurman,Mirko Primc
Publisher : American Mathematical Soc.
Page : 89 pages
File Size : 53,8 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821809235

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Annihilating Fields of Standard Modules of $\mathfrak {sl}(2, \mathbb {C})^\sim $ and Combinatorial Identities by Arne Meurman,Mirko Primc Pdf

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.

Flat Extensions of Positive Moment Matrices: Recursively Generated Relations

Raúl E. Curto,Lawrence A. Fialkow
Flat Extensions of Positive Moment Matrices Recursively Generated Relations Book PDF

Author : Raúl E. Curto,Lawrence A. Fialkow
Publisher : American Mathematical Soc.
Page : 73 pages
File Size : 54,8 Mb
Release : 1998
Category : Functions of complex variables
ISBN : 9780821808696

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Flat Extensions of Positive Moment Matrices: Recursively Generated Relations by Raúl E. Curto,Lawrence A. Fialkow Pdf

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.

Wandering Vectors for Unitary Systems and Orthogonal Wavelets

Xingde Dai,David R. Larson
Wandering Vectors for Unitary Systems and Orthogonal Wavelets Book PDF

Author : Xingde Dai,David R. Larson
Publisher : American Mathematical Soc.
Page : 82 pages
File Size : 43,7 Mb
Release : 1998
Category : Functional analysis
ISBN : 9780821808009

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Wandering Vectors for Unitary Systems and Orthogonal Wavelets by Xingde Dai,David R. Larson Pdf

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

Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies

Wolfgang Bulla,F. Gesztesy,H. Holden,G. Teschl
Algebro Geometric Quasi Periodic Finite Gap Solutions of the Toda and Kac van Moerbeke Hierarchies Book PDF

Author : Wolfgang Bulla,F. Gesztesy,H. Holden,G. Teschl
Publisher : American Mathematical Soc.
Page : 97 pages
File Size : 40,8 Mb
Release : 1998
Category : Evolution equations, Nonlinear
ISBN : 9780821808085

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Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies by Wolfgang Bulla,F. Gesztesy,H. Holden,G. Teschl Pdf

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.

Almost Automorphic and Almost Periodic Dynamics in Skew-Product Semiflows

Wenxian Shen,Yingfei Yi
Almost Automorphic and Almost Periodic Dynamics in Skew Product Semiflows Book PDF

Author : Wenxian Shen,Yingfei Yi
Publisher : American Mathematical Soc.
Page : 111 pages
File Size : 45,6 Mb
Release : 1998
Category : Flows (Differentiable dynamical systems).
ISBN : 9780821808672

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Almost Automorphic and Almost Periodic Dynamics in Skew-Product Semiflows by Wenxian Shen,Yingfei Yi Pdf

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.

Rank 3 Amalgams

Bernd Stellmacher,Franz Georg Timmesfeld
Rank 3 Amalgams Book PDF

Author : Bernd Stellmacher,Franz Georg Timmesfeld
Publisher : American Mathematical Soc.
Page : 138 pages
File Size : 50,8 Mb
Release : 1998
Category : Amalgams
ISBN : 9780821808702

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Rank 3 Amalgams by Bernd Stellmacher,Franz Georg Timmesfeld Pdf

This book is intended for graduate students and research mathematicians working in classical linear algebraic

Hopf Algebras, Polynomial Formal Groups, and Raynaud Orders

Lindsay Childs
Hopf Algebras Polynomial Formal Groups and Raynaud Orders Book PDF

Author : Lindsay Childs
Publisher : American Mathematical Soc.
Page : 118 pages
File Size : 46,8 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821810774

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Hopf Algebras, Polynomial Formal Groups, and Raynaud Orders by Lindsay Childs Pdf

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.