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Author : Palle E. T. Jørgensen,Keri A. Kornelson,Karen L. Shuman
Publisher : Unknown
Page : 105 pages
File Size : 47,8 Mb
Release : 2011
Category : MATHEMATICS
ISBN : 1470406209
Author : Palle E. T. Jørgensen,Keri A. Kornelson,Karen L. Shuman
Publisher : American Mathematical Soc.
Page : 122 pages
File Size : 55,6 Mb
Release : 2011
Category : Infinite matrices
ISBN : 9780821852484
The authors study the moments of equilibrium measures for iterated function systems (IFSs) and draw connections to operator theory. Their main object of study is the infinite matrix which encodes all the moment data of a Borel measure on $\mathbb{R}^d$ or $\mathbb{C}$. To encode the salient features of a given IFS into precise moment data, they establish an interdependence between IFS equilibrium measures, the encoding of the sequence of moments of these measures into operators, and a new correspondence between the IFS moments and this family of operators in Hilbert space. For a given IFS, the authors' aim is to establish a functorial correspondence in such a way that the geometric transformations of the IFS turn into transformations of moment matrices, or rather transformations of the operators that are associated with them.
Author : Palle E. T. Jørgensen,Keri A. Kornelson,Karen L. Shuman
Publisher : American Mathematical Soc.
Page : 122 pages
File Size : 41,5 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 9780821882481
"September 2011, volume 213, number 1003 (fourth of 5 numbers)."
Author : Sangita Jha,Mrinal Kanti Roychowdhury,Saurabh Verma
Publisher : American Mathematical Society
Page : 270 pages
File Size : 50,8 Mb
Release : 2024-04-18
Category : Mathematics
ISBN : 9781470472160
This volume contains the proceedings of the virtual AMS Special Session on Fractal Geometry and Dynamical Systems, held from May 14–15, 2022. The content covers a wide range of topics. It includes nonautonomous dynamics of complex polynomials, theory and applications of polymorphisms, topological and geometric problems related to dynamical systems, and also covers fractal dimensions, including the Hausdorff dimension of fractal interpolation functions. Furthermore, the book contains a discussion of self-similar measures as well as the theory of IFS measures associated with Bratteli diagrams. This book is suitable for graduate students interested in fractal theory, researchers interested in fractal geometry and dynamical systems, and anyone interested in the application of fractals in science and engineering. This book also offers a valuable resource for researchers working on applications of fractals in different fields.
Author : Maurice Duits,Arno B. J. Kuijlaars,Man Yue Mo
Publisher : American Mathematical Soc.
Page : 105 pages
File Size : 45,5 Mb
Release : 2012
Category : Boundary value problems
ISBN : 9780821869284
The authors consider the two matrix model with an even quartic potential $W(y)=y^4/4+\alpha y^2/2$ and an even polynomial potential $V(x)$. The main result of the paper is the formulation of a vector equilibrium problem for the limiting mean density for the eigenvalues of one of the matrices $M_1$. The vector equilibrium problem is defined for three measures, with external fields on the first and third measures and an upper constraint on the second measure. The proof is based on a steepest descent analysis of a $4\times4$ matrix valued Riemann-Hilbert problem that characterizes the correlation kernel for the eigenvalues of $M_1$. The authors' results generalize earlier results for the case $\alpha=0$, where the external field on the third measure was not present.
Author : John C. Baez
Publisher : American Mathematical Soc.
Page : 120 pages
File Size : 42,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821872840
A “$2$-group'' is a category equipped with a multiplication satisfying laws like those of a group. Just as groups have representations on vector spaces, $2$-groups have representations on “$2$-vector spaces'', which are categories analogous to vector spaces. Unfortunately, Lie $2$-groups typically have few representations on the finite-dimensional $2$-vector spaces introduced by Kapranov and Voevodsky. For this reason, Crane, Sheppeard and Yetter introduced certain infinite-dimensional $2$-vector spaces called ``measurable categories'' (since they are closely related to measurable fields of Hilbert spaces), and used these to study infinite-dimensional representations of certain Lie $2$-groups. Here they continue this work.
They begin with a detailed study of measurable categories. Then they give a geometrical description of the measurable representations, intertwiners and $2$-intertwiners for any skeletal measurable $2$-group. They study tensor products and direct sums for representations, and various concepts of subrepresentation. They describe direct sums of intertwiners, and sub-intertwiners--features not seen in ordinary group representation theory and study irreducible and indecomposable representations and intertwiners. They also study “irretractable'' representations--another feature not seen in ordinary group representation theory. Finally, they argue that measurable categories equipped with some extra structure deserve to be considered “separable $2$-Hilbert spaces'', and compare this idea to a tentative definition of $2$-Hilbert spaces as representation categories of commutative von Neumann algebras.
Author : Igor Burban,Bernd Kreussler
Publisher : American Mathematical Soc.
Page : 131 pages
File Size : 50,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821872925
"November 2012, volume 220, number 1035 (third of 4 numbers)."
Author : Daniel Allcock
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 53,8 Mb
Release : 2012-10-31
Category : Mathematics
ISBN : 9780821869116
"November 2012, volume 220, Number 1033 (first of 4 numbers)."
Author : Lee Mosher,Michah Sageev,Kevin Whyte
Publisher : American Mathematical Soc.
Page : 118 pages
File Size : 46,8 Mb
Release : 2011
Category : Geometric group theory
ISBN : 9780821847121
This paper addresses questions of quasi-isometric rigidity and classification for fundamental groups of finite graphs of groups, under the assumption that the Bass-Serre tree of the graph of groups has finite depth. The main example of a finite depth graph of groups is one whose vertex and edge groups are coarse Poincare duality groups. The main theorem says that, under certain hypotheses, if $\mathcal{G}$ is a finite graph of coarse Poincare duality groups, then any finitely generated group quasi-isometric to the fundamental group of $\mathcal{G}$ is also the fundamental group of a finite graph of coarse Poincare duality groups, and any quasi-isometry between two such groups must coarsely preserve the vertex and edge spaces of their Bass-Serre trees of spaces. Besides some simple normalization hypotheses, the main hypothesis is the ``crossing graph condition'', which is imposed on each vertex group $\mathcal{G}_v$ which is an $n$-dimensional coarse Poincare duality group for which every incident edge group has positive codimension: the crossing graph of $\mathcal{G}_v$ is a graph $\epsilon_v$ that describes the pattern in which the codimension 1 edge groups incident to $\mathcal{G}_v$ are crossed by other edge groups incident to $\mathcal{G}_v$, and the crossing graph condition requires that $\epsilon_v$ be connected or empty.
Author : Neil P. Strickland
Publisher : American Mathematical Soc.
Page : 130 pages
File Size : 41,8 Mb
Release : 2011
Category : Algebraic geometry
ISBN : 9780821849019
Let $A$ be a finite abelian group. The author sets up an algebraic framework for studying $A$-equivariant complex-orientable cohomology theories in terms of a suitable kind of equivariant formal group. He computes the equivariant cohomology of many spaces in these terms, including projective bundles (and associated Gysin maps), Thom spaces, and infinite Grassmannians.
Author : Toshiyuki Kobayashi,Gen Mano
Publisher : American Mathematical Soc.
Page : 145 pages
File Size : 41,5 Mb
Release : 2011
Category : Representations of Lie groups
ISBN : 9780821847572
The authors introduce a generalization of the Fourier transform, denoted by $\mathcal{F}_C$, on the isotropic cone $C$ associated to an indefinite quadratic form of signature $(n_1,n_2)$ on $\mathbb{R}^n$ ($n=n_1+n_2$: even). This transform is in some sense the unique and natural unitary operator on $L^2(C)$, as is the case with the Euclidean Fourier transform $\mathcal{F}_{\mathbb{R}^n}$ on $L^2(\mathbb{R}^n)$. Inspired by recent developments of algebraic representation theory of reductive groups, the authors shed new light on classical analysis on the one hand, and give the global formulas for the $L^2$-model of the minimal representation of the simple Lie group $G=O(n_1+1,n_2+1)$ on the other hand.
Author : Michael Handel,Lee Mosher
Publisher : American Mathematical Soc.
Page : 117 pages
File Size : 50,9 Mb
Release : 2011
Category : Geometric group theory
ISBN : 9780821869277
"September 2011, volume 213, number 1004 (end of volume)."
Author : Nicola Gigli
Publisher : American Mathematical Soc.
Page : 173 pages
File Size : 51,9 Mb
Release : 2012-02-22
Category : Mathematics
ISBN : 9780821853092
The author develops a rigorous second order analysis on the space of probability measures on a Riemannian manifold endowed with the quadratic optimal transport distance $W_2$. The discussion includes: definition of covariant derivative, discussion of the problem of existence of parallel transport, calculus of the Riemannian curvature tensor, differentiability of the exponential map and existence of Jacobi fields. This approach does not require any smoothness assumption on the measures considered.
Author : Christophe Breuil,Vytautas Paskunas
Publisher : American Mathematical Soc.
Page : 127 pages
File Size : 42,7 Mb
Release : 2012-02-22
Category : Mathematics
ISBN : 9780821852279
The authors construct new families of smooth admissible $\overline{\mathbb{F}}_p$-representations of $\mathrm{GL}_2(F)$, where $F$ is a finite extension of $\mathbb{Q}_p$. When $F$ is unramified, these representations have the $\mathrm{GL}_2({\mathcal O}_F)$-socle predicted by the recent generalizations of Serre's modularity conjecture. The authors' motivation is a hypothetical mod $p$ Langlands correspondence.
Author : Man Chun Leung
Publisher : American Mathematical Soc.
Page : 112 pages
File Size : 43,5 Mb
Release : 2011
Category : Blowing up (Algebraic geometry).
ISBN : 9780821853375
The author expounds the notion of supported blow-up and applies it to study the renowned Nirenberg/Kazdan-Warner problem on $S^n$. When $n \ge 5$ and under some mild conditions, he shows that blow-up at a point with positive definite Hessian has to be a supported isolated blow-up, which, when combined with a uniform volume bound, is a removable singularity. A new asymmetric condition is introduced to exclude single simple blow-up. These enable the author to obtain a general existence theorem for $n \ge 5$ with rather natural condition.
