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Author : Simon N. Chandler-Wilde,Marko Lindner
Publisher : Unknown
Page : 0 pages
File Size : 52,9 Mb
Release : 2008
Category : Electronic
ISBN : OCLC:261411997
Author : Simon N. Chandler-Wilde,Marko Lindner
Publisher : American Mathematical Soc.
Page : 126 pages
File Size : 47,8 Mb
Release : 2024-07-02
Category : Mathematics
ISBN : 9780821874165
An exploration of the interrelationships netween the abstract theory of limit operators and the concepts and results of the generalised collectively compact operator theory. This book also looks at at bounded linear operators and the connections between Fredholmness and invertibility.
Author : Simon N. Chandler-Wilde,Marko Lindner
Publisher : American Mathematical Soc.
Page : 126 pages
File Size : 50,9 Mb
Release : 2011
Category : Compact operators
ISBN : 9780821852439
In the first half of this memoir the authors explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch and Silbermann (2004) and Lindner (2006)) and the concepts and results of the generalised collectively compact operator theory introduced by Chandler-Wilde and Zhang (2002). They build up to results obtained by applying this generalised collectively compact operator theory to the set of limit operators of an operator $A$ (its operator spectrum). In the second half of this memoir the authors study bounded linear operators on the generalised sequence space $\ell^p(\mathbb{Z}^N,U)$, where $p\in [1,\infty]$ and $U$ is some complex Banach space. They make what seems to be a more complete study than hitherto of the connections between Fredholmness, invertibility, invertibility at infinity, and invertibility or injectivity of the set of limit operators, with some emphasis on the case when the operator $A$ is a locally compact perturbation of the identity. Especially, they obtain stronger results than previously known for the subtle limiting cases of $p=1$ and $\infty$.
Author : Yemon Choi,Matthew Daws,Gordon Blower
Publisher : Springer Nature
Page : 262 pages
File Size : 54,7 Mb
Release : 2023-12-06
Category : Mathematics
ISBN : 9783031380204
This volume collects contributions from participants in the IWOTA conference held virtually at Lancaster, UK, originally scheduled in 2020 but postponed to August 2021. It includes both survey articles and original research papers covering some of the main themes of the meeting.
Author : Palle E. T. Jørgensen,Keri A. Kornelson,Karen L. Shuman
Publisher : American Mathematical Soc.
Page : 122 pages
File Size : 44,7 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 : Radu Balan,Matthew J. Begué,John J. Benedetto,Wojciech Czaja,Kasso A. Okoudjou
Publisher : Birkhäuser
Page : 336 pages
File Size : 47,5 Mb
Release : 2015-06-02
Category : Mathematics
ISBN : 9783319132303
This volume consists of contributions spanning a wide spectrum of harmonic analysis and its applications written by speakers at the February Fourier Talks from 2002 – 2013. Containing cutting-edge results by an impressive array of mathematicians, engineers, and scientists in academia, industry, and government, it will be an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, physics, and engineering. Topics covered include · spectral analysis and correlation; · radar and communications: design, theory, and applications; · sparsity · special topics in harmonic analysis. The February Fourier Talks are held annually at the Norbert Wiener Center for Harmonic Analysis and Applications. Located at the University of Maryland, College Park, the Norbert Wiener Center provides a state-of- the-art research venue for the broad emerging area of mathematical engineering.
Author : Marko Lindner
Publisher : Springer Science & Business Media
Page : 203 pages
File Size : 48,6 Mb
Release : 2006-11-10
Category : Mathematics
ISBN : 9783764377670
This book is concerned with the study of infinite matrices and their approximation by matrices of finite size. The main concepts presented are invertibility at infinity (closely related to Fredholmness), limit operators, and the stability and convergence of finite matrix approximations. Concrete examples are used to illustrate the results throughout, including discrete Schrödinger operators and integral and boundary integral operators arising in mathematical physics and engineering.
Author : John C. Baez
Publisher : American Mathematical Soc.
Page : 120 pages
File Size : 43,6 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 : Maurice Duits,Arno B. J. Kuijlaars,Man Yue Mo
Publisher : American Mathematical Soc.
Page : 105 pages
File Size : 48,8 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 : Hideki Kosaki
Publisher : American Mathematical Soc.
Page : 93 pages
File Size : 49,8 Mb
Release : 2011-06-10
Category : Mathematics
ISBN : 9780821853078
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 : Neil P. Strickland
Publisher : American Mathematical Soc.
Page : 130 pages
File Size : 43,6 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 : 44,6 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 : 50,5 Mb
Release : 2011
Category : Geometric group theory
ISBN : 9780821869277
"September 2011, volume 213, number 1004 (end of volume)."
Author : Igor Burban,Bernd Kreussler
Publisher : American Mathematical Soc.
Page : 131 pages
File Size : 42,9 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 : 45,6 Mb
Release : 2012-10-31
Category : Mathematics
ISBN : 9780821869116
"November 2012, volume 220, Number 1033 (first of 4 numbers)."