Classification Of E 0 Semigroups By Product Systems
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Classification Of E 0 Semigroups By Product Systems
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Author : Michael Skeide
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-03-10
Classification Of E 0 Semigroups By Product Systems written by Michael Skeide and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-10 with Mathematics categories.
In these notes the author presents a complete theory of classification of E0-semigroups by product systems of correspondences. As an application of his theory, he answers the fundamental question if a Markov semigroup admits a dilation by a cocycle perturbations of noise: It does if and only if it is spatial.
Noncommutative Dynamics And E Semigroups
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Author : William Arveson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-06
Noncommutative Dynamics And E Semigroups written by William Arveson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-06 with Mathematics categories.
These days, the term Noncommutative Dynamics has several interpretations. It is used in this book to refer to a set of phenomena associated with the dynamical evo lution of quantum systems of the simplest kind that involve rigorous mathematical structures associated with infinitely many degrees of freedom. The dynamics of such a system is represented by a one-parameter group of automorphisms of a non commutative algebra of observables, and we focus primarily on the most concrete case in which that algebra consists of all bounded operators on a Hilbert space. If one introduces a natural causal structure into such a dynamical system, then a pair of one-parameter semigroups of endomorphisms emerges, and it is useful to think of this pair as representing the past and future with respect to the given causality. These are both Eo-semigroups, and to a great extent the problem of understanding such causal dynamical systems reduces to the problem of under standing Eo-semigroups. The nature of these connections is discussed at length in Chapter 1. The rest of the book elaborates on what the author sees as the impor tant aspects of what has been learned about Eo-semigroups during the past fifteen years. Parts of the subject have evolved into a satisfactory theory with effective toolsj other parts remain quite mysterious. Like von Neumann algebras, Eo-semigroups divide naturally into three types: 1,11,111.
Problems In The Classification Of E0 Semigroups
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Author : Masayasu Aotani
language : en
Publisher:
Release Date : 1996
Problems In The Classification Of E0 Semigroups written by Masayasu Aotani and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
Rectifiable Measures Square Functions Involving Densities And The Cauchy Transform
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Author : Xavier Tolsa
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-01-18
Rectifiable Measures Square Functions Involving Densities And The Cauchy Transform written by Xavier Tolsa and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-18 with Mathematics categories.
This monograph is devoted to the proof of two related results. The first one asserts that if is a Radon measure in satisfyingfor -a.e. , then is rectifiable. Since the converse implication is already known to hold, this yields the following characterization of rectifiable sets: a set with finite -dimensional Hausdorff measure is rectifiable if and only ifH^1x2EThe second result of the monograph deals with the relationship between the above square function in the complex plane and the Cauchy transform . Assuming that has linear growth, it is proved that is bounded in if and only iffor every square .
Imaginary Schur Weyl Duality
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Author : Alexander Kleshchev
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-01-18
Imaginary Schur Weyl Duality written by Alexander Kleshchev and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-18 with Mathematics categories.
The authors study imaginary representations of the Khovanov-Lauda-Rouquier algebras of affine Lie type. Irreducible modules for such algebras arise as simple heads of standard modules. In order to define standard modules one needs to have a cuspidal system for a fixed convex preorder. A cuspidal system consists of irreducible cuspidal modules—one for each real positive root for the corresponding affine root system X , as well as irreducible imaginary modules—one for each -multiplication. The authors study imaginary modules by means of “imaginary Schur-Weyl duality” and introduce an imaginary analogue of tensor space and the imaginary Schur algebra. They construct a projective generator for the imaginary Schur algebra, which yields a Morita equivalence between the imaginary and the classical Schur algebra, and construct imaginary analogues of Gelfand-Graev representations, Ringel duality and the Jacobi-Trudy formula.
Exotic Cluster Structures On Sl N The Cremmer Gervais Case
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Author : M. Gekhtman
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-02-20
Exotic Cluster Structures On Sl N The Cremmer Gervais Case written by M. Gekhtman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-20 with Mathematics categories.
This is the second paper in the series of papers dedicated to the study of natural cluster structures in the rings of regular functions on simple complex Lie groups and Poisson–Lie structures compatible with these cluster structures. According to our main conjecture, each class in the Belavin–Drinfeld classification of Poisson–Lie structures on corresponds to a cluster structure in . The authors have shown before that this conjecture holds for any in the case of the standard Poisson–Lie structure and for all Belavin–Drinfeld classes in , . In this paper the authors establish it for the Cremmer–Gervais Poisson–Lie structure on , which is the least similar to the standard one.
Homology Of Normal Chains And Cohomology Of Charges
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Author : Th. De Pauw
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-04-25
Homology Of Normal Chains And Cohomology Of Charges written by Th. De Pauw and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-25 with Mathematics categories.
The authors consider a category of pairs of compact metric spaces and Lipschitz maps where the pairs satisfy a linearly isoperimetric condition related to the solvability of the Plateau problem with partially free boundary. It includes properly all pairs of compact Lipschitz neighborhood retracts of a large class of Banach spaces. On this category the authors define homology and cohomology functors with real coefficients which satisfy the Eilenberg-Steenrod axioms, but reflect the metric properties of the underlying spaces. As an example they show that the zero-dimensional homology of a space in our category is trivial if and only if the space is path connected by arcs of finite length. The homology and cohomology of a pair are, respectively, locally convex and Banach spaces that are in duality. Ignoring the topological structures, the homology and cohomology extend to all pairs of compact metric spaces. For locally acyclic spaces, the authors establish a natural isomorphism between their cohomology and the Čech cohomology with real coefficients.
New Foundations For Geometry Two Non Additive Languages For Arithmetical Geometry
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Author : Shai M. J. Haran
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-02-20
New Foundations For Geometry Two Non Additive Languages For Arithmetical Geometry written by Shai M. J. Haran and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-20 with Mathematics categories.
To view the abstract go to http://www.ams.org/books/memo/1166.
The Mathematics Of Superoscillations
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Author : Yakir Aharonov
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-04-25
The Mathematics Of Superoscillations written by Yakir Aharonov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-25 with Mathematics categories.
In the past 50 years, quantum physicists have discovered, and experimentally demonstrated, a phenomenon which they termed superoscillations. Aharonov and his collaborators showed that superoscillations naturally arise when dealing with weak values, a notion that provides a fundamentally different way to regard measurements in quantum physics. From a mathematical point of view, superoscillating functions are a superposition of small Fourier components with a bounded Fourier spectrum, which result, when appropriately summed, in a shift that can be arbitrarily large, and well outside the spectrum. The purpose of this work is twofold: on one hand the authors provide a self-contained survey of the existing literature, in order to offer a systematic mathematical approach to superoscillations; on the other hand, they obtain some new and unexpected results, by showing that superoscillating sequences can be seen of as solutions to a large class of convolution equations and can therefore be treated within the theory of analytically uniform spaces. In particular, the authors will also discuss the persistence of the superoscillatory behavior when superoscillating sequences are taken as initial values of the Schrödinger equation and other equations.
The Role Of Advection In A Two Species Competition Model A Bifurcation Approach
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Author : Isabel Averill
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-01-18
The Role Of Advection In A Two Species Competition Model A Bifurcation Approach written by Isabel Averill and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-18 with Mathematics categories.
The effects of weak and strong advection on the dynamics of reaction-diffusion models have long been studied. In contrast, the role of intermediate advection remains poorly understood. For example, concentration phenomena can occur when advection is strong, providing a mechanism for the coexistence of multiple populations, in contrast with the situation of weak advection where coexistence may not be possible. The transition of the dynamics from weak to strong advection is generally difficult to determine. In this work the authors consider a mathematical model of two competing populations in a spatially varying but temporally constant environment, where both species have the same population dynamics but different dispersal strategies: one species adopts random dispersal, while the dispersal strategy for the other species is a combination of random dispersal and advection upward along the resource gradient. For any given diffusion rates the authors consider the bifurcation diagram of positive steady states by using the advection rate as the bifurcation parameter. This approach enables the authors to capture the change of dynamics from weak advection to strong advection. The authors determine three different types of bifurcation diagrams, depending on the difference of diffusion rates. Some exact multiplicity results about bifurcation points are also presented. The authors' results can unify some previous work and, as a case study about the role of advection, also contribute to the understanding of intermediate (relative to diffusion) advection in reaction-diffusion models.