Q Valued Functions Revisited

Author : Camillo De Lellis,Emanuele Nunzio Spadaro
Publisher : American Mathematical Soc.
Page : 92 pages
File Size : 54,8 Mb
Release : 2011
Category : Dirichlet principle
ISBN : 9780821849149

Get Book

$Q$-Valued Functions Revisited by Camillo De Lellis,Emanuele Nunzio Spadaro Pdf

In this memoir the authors revisit Almgren's theory of $Q$-valued functions, which are functions taking values in the space $\mathcal{A}_Q(\mathbb{R}^{n})$ of unordered $Q$-tuples of points in $\mathbb{R}^{n}$. In particular, the authors: give shorter versions of Almgren's proofs of the existence of $\mathrm{Dir}$-minimizing $Q$-valued functions, of their Holder regularity, and of the dimension estimate of their singular set; propose an alternative, intrinsic approach to these results, not relying on Almgren's biLipschitz embedding $\xi: \mathcal{A}_Q(\mathbb{R}^{n})\to\mathbb{R}^{N(Q,n)}$; improve upon the estimate of the singular set of planar $\mathrm{D}$-minimizing functions by showing that it consists of isolated points.

Author : Carlos E. Kenig
Publisher : American Mathematical Soc.
Page : 345 pages
File Size : 43,9 Mb
Release : 2020-12-14
Category : Education
ISBN : 9781470461270

Get Book

Harmonic Analysis and Applications by Carlos E. Kenig Pdf

The origins of the harmonic analysis go back to an ingenious idea of Fourier that any reasonable function can be represented as an infinite linear combination of sines and cosines. Today's harmonic analysis incorporates the elements of geometric measure theory, number theory, probability, and has countless applications from data analysis to image recognition and from the study of sound and vibrations to the cutting edge of contemporary physics. The present volume is based on lectures presented at the summer school on Harmonic Analysis. These notes give fresh, concise, and high-level introductions to recent developments in the field, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field and to senior researchers wishing to keep up with current developments.

Author : Anonim
Publisher : World Scientific
Page : 1001 pages
File Size : 49,8 Mb
Release : 2024-06-29
Category : Electronic
ISBN : 8210379456XXX

Get Book

by Anonim Pdf

Author : Bhatia Rajendra,Pal Arup,Rangarajan G
Publisher : World Scientific
Page : 4144 pages
File Size : 41,7 Mb
Release : 2011-06-06
Category : Mathematics
ISBN : 9789814462938

Get Book

Proceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures by Bhatia Rajendra,Pal Arup,Rangarajan G Pdf

ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.

Author : Palle E. T. Jørgensen,Keri A. Kornelson,Karen L. Shuman
Publisher : American Mathematical Soc.
Page : 122 pages
File Size : 43,7 Mb
Release : 2011
Category : Infinite matrices
ISBN : 9780821852484

Get Book

Iterated Function Systems, Moments, and Transformations of Infinite Matrices by Palle E. T. Jørgensen,Keri A. Kornelson,Karen L. Shuman Pdf

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 : Toshiyuki Kobayashi,Gen Mano
Publisher : American Mathematical Soc.
Page : 145 pages
File Size : 40,6 Mb
Release : 2011
Category : Representations of Lie groups
ISBN : 9780821847572

Get Book

The Schrodinger Model for the Minimal Representation of the Indefinite Orthogonal Group $O(p,q)$ by Toshiyuki Kobayashi,Gen Mano Pdf

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 : Jan de Gier,Cheryl E. Praeger,Terence Tao
Publisher : Springer
Page : 691 pages
File Size : 55,7 Mb
Release : 2019-03-13
Category : Mathematics
ISBN : 9783030041618

Get Book

2017 MATRIX Annals by Jan de Gier,Cheryl E. Praeger,Terence Tao Pdf

​MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the eight programs held at MATRIX in its second year, 2017: - Hypergeometric Motives and Calabi–Yau Differential Equations - Computational Inverse Problems - Integrability in Low-Dimensional Quantum Systems - Elliptic Partial Differential Equations of Second Order: Celebrating 40 Years of Gilbarg and Trudinger’s Book - Combinatorics, Statistical Mechanics, and Conformal Field Theory - Mathematics of Risk - Tutte Centenary Retreat - Geometric R-Matrices: from Geometry to Probability The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.

Author : Hideki Kosaki
Publisher : American Mathematical Soc.
Page : 93 pages
File Size : 50,6 Mb
Release : 2011-06-10
Category : Mathematics
ISBN : 9780821853078

Get Book

Positive Definiteness of Functions with Applications to Operator Norm Inequalities by Hideki Kosaki Pdf

Positive definiteness is determined for a wide class of functions relevant in the study of operator means and their norm comparisons. Then, this information is used to obtain an abundance of new sharp (unitarily) norm inequalities comparing various operator means and sometimes other related operators.

Author : Igor Burban,Bernd Kreussler
Publisher : American Mathematical Soc.
Page : 131 pages
File Size : 52,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821872925

Get Book

Vector Bundles on Degenerations of Elliptic Curves and Yang-Baxter Equations by Igor Burban,Bernd Kreussler Pdf

"November 2012, volume 220, number 1035 (third of 4 numbers)."

Author : Neil P. Strickland
Publisher : American Mathematical Soc.
Page : 130 pages
File Size : 42,5 Mb
Release : 2011
Category : Algebraic geometry
ISBN : 9780821849019

Get Book

Multicurves and Equivariant Cohomology by Neil P. Strickland Pdf

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 : Daniel Allcock
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 42,7 Mb
Release : 2012-10-31
Category : Mathematics
ISBN : 9780821869116

Get Book

The Reflective Lorentzian Lattices of Rank 3 by Daniel Allcock Pdf

"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 : 53,8 Mb
Release : 2011
Category : Geometric group theory
ISBN : 9780821847121

Get Book

Quasi-Actions on Trees II: Finite Depth Bass-Serre Trees by Lee Mosher,Michah Sageev,Kevin Whyte Pdf

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 : Michael Handel,Lee Mosher
Publisher : American Mathematical Soc.
Page : 117 pages
File Size : 42,7 Mb
Release : 2011
Category : Geometric group theory
ISBN : 9780821869277

Get Book

Axes in Outer Space by Michael Handel,Lee Mosher Pdf

"September 2011, volume 213, number 1004 (end of volume)."

Author : John C. Baez
Publisher : American Mathematical Soc.
Page : 120 pages
File Size : 53,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821872840

Get Book

Infinite-dimensional Representations of 2-groups by John C. Baez Pdf

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 : Mikhail Khovanov
Publisher : American Mathematical Soc.
Page : 87 pages
File Size : 48,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821889770

Get Book

Extended Graphical Calculus for Categorified Quantum Sl(2) by Mikhail Khovanov Pdf

A categorification of the Beilinson-Lusztig-MacPherson form of the quantum sl(2) was constructed in a paper (arXiv:0803.3652) by Aaron D. Lauda. Here the authors enhance the graphical calculus introduced and developed in that paper to include two-morphisms between divided powers one-morphisms and their compositions. They obtain explicit diagrammatical formulas for the decomposition of products of divided powers one-morphisms as direct sums of indecomposable one-morphisms; the latter are in a bijection with the Lusztig canonical basis elements.

These formulas have integral coefficients and imply that one of the main results of Lauda's paper--identification of the Grothendieck ring of his 2-category with the idempotented quantum sl(2)--also holds when the 2-category is defined over the ring of integers rather than over a field. A new diagrammatic description of Schur functions is also given and it is shown that the the Jacobi-Trudy formulas for the decomposition of Schur functions into elementary or complete symmetric functions follows from the diagrammatic relations for categorified quantum sl(2).