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Author : Toshihiko Masuda
Publisher :
ISBN 13 : 9781470435066
Total Pages : pages
Book Rating : 4.4/5 (35 download)
Download or read book Rohlin Flows on Von Neumann Algebras written by Toshihiko Masuda and published by . This book was released on 2016-11-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Toshihiko Masuda
Publisher : American Mathematical Soc.
ISBN 13 : 1470420163
Total Pages : 128 pages
Book Rating : 4.4/5 (74 download)
Download or read book Rohlin Flows on von Neumann Algebras written by Toshihiko Masuda and published by American Mathematical Soc.. This book was released on 2016-10-05 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors will classify Rohlin flows on von Neumann algebras up to strong cocycle conjugacy. This result provides alternative approaches to some preceding results such as Kawahigashi's classification of flows on the injective type II1 factor, the classification of injective type III factors due to Connes, Krieger and Haagerup and the non-fullness of type III0 factors. Several concrete examples are also studied.
Author : Toshihiko Masuda
Publisher : American Mathematical Soc.
ISBN 13 : 1470420554
Total Pages : 134 pages
Book Rating : 4.4/5 (74 download)
Download or read book Classification of Actions of Discrete Kac Algebras on Injective Factors written by Toshihiko Masuda and published by American Mathematical Soc.. This book was released on 2017-01-18 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study two kinds of actions of a discrete amenable Kac algebra. The first one is an action whose modular part is normal. They construct a new invariant which generalizes a characteristic invariant for a discrete group action, and we will present a complete classification. The second is a centrally free action. By constructing a Rohlin tower in an asymptotic centralizer, the authors show that the Connes–Takesaki module is a complete invariant.
Author : Kenneth R. Davidson
Publisher : American Mathematical Soc.
ISBN 13 : 147042309X
Total Pages : 110 pages
Book Rating : 4.4/5 (74 download)
Download or read book Semicrossed Products of Operator Algebras by Semigroups written by Kenneth R. Davidson and published by American Mathematical Soc.. This book was released on 2017-04-25 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors examine the semicrossed products of a semigroup action by -endomorphisms on a C*-algebra, or more generally of an action on an arbitrary operator algebra by completely contractive endomorphisms. The choice of allowable representations affects the corresponding universal algebra. The authors seek quite general conditions which will allow them to show that the C*-envelope of the semicrossed product is (a full corner of) a crossed product of an auxiliary C*-algebra by a group action. Their analysis concerns a case-by-case dilation theory on covariant pairs. In the process we determine the C*-envelope for various semicrossed products of (possibly nonselfadjoint) operator algebras by spanning cones and lattice-ordered abelian semigroups.
Author : Yakir Aharonov
Publisher : American Mathematical Soc.
ISBN 13 : 1470423243
Total Pages : 120 pages
Book Rating : 4.4/5 (74 download)
Download or read book The Mathematics of Superoscillations written by Yakir Aharonov and published by American Mathematical Soc.. This book was released on 2017-04-25 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Xavier Tolsa
Publisher : American Mathematical Soc.
ISBN 13 : 1470422522
Total Pages : 142 pages
Book Rating : 4.4/5 (74 download)
Download or read book Rectifiable Measures, Square Functions Involving Densities, and the Cauchy Transform written by Xavier Tolsa and published by American Mathematical Soc.. This book was released on 2017-01-18 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 .
Author : Isabel Averill
Publisher : American Mathematical Soc.
ISBN 13 : 1470422026
Total Pages : 118 pages
Book Rating : 4.4/5 (74 download)
Download or read book The Role of Advection in a Two-Species Competition Model: A Bifurcation Approach written by Isabel Averill and published by American Mathematical Soc.. This book was released on 2017-01-18 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : M. Gekhtman
Publisher : American Mathematical Soc.
ISBN 13 : 1470422581
Total Pages : 106 pages
Book Rating : 4.4/5 (74 download)
Download or read book Exotic Cluster Structures on $SL_n$: The Cremmer-Gervais Case written by M. Gekhtman and published by American Mathematical Soc.. This book was released on 2017-02-20 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Steve Hofmann
Publisher : American Mathematical Soc.
ISBN 13 : 1470422603
Total Pages : 120 pages
Book Rating : 4.4/5 (74 download)
Download or read book $L^p$-Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets written by Steve Hofmann and published by American Mathematical Soc.. This book was released on 2017-01-18 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors establish square function estimates for integral operators on uniformly rectifiable sets by proving a local theorem and applying it to show that such estimates are stable under the so-called big pieces functor. More generally, they consider integral operators associated with Ahlfors-David regular sets of arbitrary codimension in ambient quasi-metric spaces. The local theorem is then used to establish an inductive scheme in which square function estimates on so-called big pieces of an Ahlfors-David regular set are proved to be sufficient for square function estimates to hold on the entire set. Extrapolation results for and Hardy space versions of these estimates are also established. Moreover, the authors prove square function estimates for integral operators associated with variable coefficient kernels, including the Schwartz kernels of pseudodifferential operators acting between vector bundles on subdomains with uniformly rectifiable boundaries on manifolds.
Author : F. Dahmani
Publisher : American Mathematical Soc.
ISBN 13 : 1470421941
Total Pages : 164 pages
Book Rating : 4.4/5 (74 download)
Download or read book Hyperbolically Embedded Subgroups and Rotating Families in Groups Acting on Hyperbolic Spaces written by F. Dahmani and published by American Mathematical Soc.. This book was released on 2017-01-18 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: he authors introduce and study the notions of hyperbolically embedded and very rotating families of subgroups. The former notion can be thought of as a generalization of the peripheral structure of a relatively hyperbolic group, while the latter one provides a natural framework for developing a geometric version of small cancellation theory. Examples of such families naturally occur in groups acting on hyperbolic spaces including hyperbolic and relatively hyperbolic groups, mapping class groups, , and the Cremona group. Other examples can be found among groups acting geometrically on spaces, fundamental groups of graphs of groups, etc. The authors obtain a number of general results about rotating families and hyperbolically embedded subgroups; although their technique applies to a wide class of groups, it is capable of producing new results even for well-studied particular classes. For instance, the authors solve two open problems about mapping class groups, and obtain some results which are new even for relatively hyperbolic groups.
Author : Alexander Kleshchev
Publisher : American Mathematical Soc.
ISBN 13 : 1470422492
Total Pages : 108 pages
Book Rating : 4.4/5 (74 download)
Download or read book Imaginary Schur-Weyl Duality written by Alexander Kleshchev and published by American Mathematical Soc.. This book was released on 2017-01-18 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Th. De Pauw
Publisher : American Mathematical Soc.
ISBN 13 : 1470423359
Total Pages : 128 pages
Book Rating : 4.4/5 (74 download)
Download or read book Homology of Normal Chains and Cohomology of Charges written by Th. De Pauw and published by American Mathematical Soc.. This book was released on 2017-04-25 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Charles Fefferman
Publisher : American Mathematical Soc.
ISBN 13 : 1470423235
Total Pages : 132 pages
Book Rating : 4.4/5 (74 download)
Download or read book Topologically Protected States in One-Dimensional Systems written by Charles Fefferman and published by American Mathematical Soc.. This book was released on 2017-04-25 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study a class of periodic Schrodinger operators, which in distinguished cases can be proved to have linear band-crossings or ``Dirac points''. They then show that the introduction of an ``edge'', via adiabatic modulation of these periodic potentials by a domain wall, results in the bifurcation of spatially localized ``edge states''. These bound states are associated with the topologically protected zero-energy mode of an asymptotic one-dimensional Dirac operator. The authors' model captures many aspects of the phenomenon of topologically protected edge states for two-dimensional bulk structures such as the honeycomb structure of graphene. The states the authors construct can be realized as highly robust TM-electromagnetic modes for a class of photonic waveguides with a phase-defect.
Author : Matthew J. Emerton
Publisher : American Mathematical Soc.
ISBN 13 : 0821875620
Total Pages : 168 pages
Book Rating : 4.8/5 (218 download)
Download or read book Locally Analytic Vectors in Representations of Locally $p$-adic Analytic Groups written by Matthew J. Emerton and published by American Mathematical Soc.. This book was released on 2017-07-13 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this memoir is to provide the foundations for the locally analytic representation theory that is required in three of the author's other papers on this topic. In the course of writing those papers the author found it useful to adopt a particular point of view on locally analytic representation theory: namely, regarding a locally analytic representation as being the inductive limit of its subspaces of analytic vectors (of various “radii of analyticity”). The author uses the analysis of these subspaces as one of the basic tools in his study of such representations. Thus in this memoir he presents a development of locally analytic representation theory built around this point of view. The author has made a deliberate effort to keep the exposition reasonably self-contained and hopes that this will be of some benefit to the reader.
Author : Thierry Daudé
Publisher : American Mathematical Soc.
ISBN 13 : 1470423766
Total Pages : 126 pages
Book Rating : 4.4/5 (74 download)
Download or read book Direct and Inverse Scattering at Fixed Energy for Massless Charged Dirac Fields by Kerr-Newman-de Sitter Black Holes written by Thierry Daudé and published by American Mathematical Soc.. This book was released on 2017-04-25 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the authors study the direct and inverse scattering theory at fixed energy for massless charged Dirac fields evolving in the exterior region of a Kerr-Newman-de Sitter black hole. In the first part, they establish the existence and asymptotic completeness of time-dependent wave operators associated to our Dirac fields. This leads to the definition of the time-dependent scattering operator that encodes the far-field behavior (with respect to a stationary observer) in the asymptotic regions of the black hole: the event and cosmological horizons. The authors also use the miraculous property (quoting Chandrasekhar)—that the Dirac equation can be separated into radial and angular ordinary differential equations—to make the link between the time-dependent scattering operator and its stationary counterpart. This leads to a nice expression of the scattering matrix at fixed energy in terms of stationary solutions of the system of separated equations. In a second part, the authors use this expression of the scattering matrix to study the uniqueness property in the associated inverse scattering problem at fixed energy. Using essentially the particular form of the angular equation (that can be solved explicitly by Frobenius method) and the Complex Angular Momentum technique on the radial equation, the authors are finally able to determine uniquely the metric of the black hole from the knowledge of the scattering matrix at a fixed energy.
Author : Yves Le Jan
Publisher : American Mathematical Soc.
ISBN 13 : 1470436957
Total Pages : 92 pages
Book Rating : 4.4/5 (74 download)
Download or read book Intersection Local Times, Loop Soups and Permanental Wick Powers written by Yves Le Jan and published by American Mathematical Soc.. This book was released on 2017-04-25 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several stochastic processes related to transient Lévy processes with potential densities , that need not be symmetric nor bounded on the diagonal, are defined and studied. They are real valued processes on a space of measures endowed with a metric . Sufficient conditions are obtained for the continuity of these processes on . The processes include -fold self-intersection local times of transient Lévy processes and permanental chaoses, which are `loop soup -fold self-intersection local times' constructed from the loop soup of the Lévy process. Loop soups are also used to define permanental Wick powers, which generalizes standard Wick powers, a class of -th order Gaussian chaoses. Dynkin type isomorphism theorems are obtained that relate the various processes. Poisson chaos processes are defined and permanental Wick powers are shown to have a Poisson chaos decomposition. Additional properties of Poisson chaos processes are studied and a martingale extension is obtained for many of the processes described above.
Author : E. Delaygue
Publisher : American Mathematical Soc.
ISBN 13 : 1470423006
Total Pages : 106 pages
Book Rating : 4.4/5 (74 download)
Download or read book On Dwork's $p$-Adic Formal Congruences Theorem and Hypergeometric Mirror Maps written by E. Delaygue and published by American Mathematical Soc.. This book was released on 2017-02-20 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using Dwork's theory, the authors prove a broad generalization of his famous -adic formal congruences theorem. This enables them to prove certain -adic congruences for the generalized hypergeometric series with rational parameters; in particular, they hold for any prime number and not only for almost all primes. Furthermore, using Christol's functions, the authors provide an explicit formula for the “Eisenstein constant” of any hypergeometric series with rational parameters. As an application of these results, the authors obtain an arithmetic statement “on average” of a new type concerning the integrality of Taylor coefficients of the associated mirror maps. It contains all the similar univariate integrality results in the literature, with the exception of certain refinements that hold only in very particular cases.
