Operator Methods in Wavelets, Tilings, and Frames

Operator Methods in Wavelets, Tilings, and Frames
Author :
Publisher : American Mathematical Soc.
Total Pages : 192
Release :
ISBN-10 : 9781470410407
ISBN-13 : 1470410400
Rating : 4/5 (07 Downloads)

Synopsis Operator Methods in Wavelets, Tilings, and Frames by : Keri A. Kornelson

This volume contains the proceedings of the AMS Special Session on Harmonic Analysis of Frames, Wavelets, and Tilings, held April 13-14, 2013, in Boulder, Colorado. Frames were first introduced by Duffin and Schaeffer in 1952 in the context of nonharmonic Fourier series but have enjoyed widespread interest in recent years, particularly as a unifying concept. Indeed, mathematicians with backgrounds as diverse as classical and modern harmonic analysis, Banach space theory, operator algebras, and complex analysis have recently worked in frame theory. Frame theory appears in the context of wavelets, spectra and tilings, sampling theory, and more. The papers in this volume touch on a wide variety of topics, including: convex geometry, direct integral decompositions, Beurling density, operator-valued measures, and splines. These varied topics arise naturally in the study of frames in finite and infinite dimensions. In nearly all of the papers, techniques from operator theory serve as crucial tools to solving problems in frame theory. This volume will be of interest not only to researchers in frame theory but also to those in approximation theory, representation theory, functional analysis, and harmonic analysis.

Function Spaces in Analysis

Function Spaces in Analysis
Author :
Publisher : American Mathematical Soc.
Total Pages : 301
Release :
ISBN-10 : 9781470416942
ISBN-13 : 1470416948
Rating : 4/5 (42 Downloads)

Synopsis Function Spaces in Analysis by : Krzysztof Jarosz

This volume contains the proceedings of the Seventh Conference on Function Spaces, which was held from May 20-24, 2014 at Southern Illinois University at Edwardsville. The papers cover a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), spaces of integrable functions, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects.

Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions

Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions
Author :
Publisher : American Mathematical Soc.
Total Pages : 118
Release :
ISBN-10 : 9781470434557
ISBN-13 : 1470434555
Rating : 4/5 (57 Downloads)

Synopsis Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions by : J. William Helton

An operator C on a Hilbert space H dilates to an operator T on a Hilbert space K if there is an isometry V:H→K such that C=V∗TV. A main result of this paper is, for a positive integer d, the simultaneous dilation, up to a sharp factor ϑ(d), expressed as a ratio of Γ functions for d even, of all d×d symmetric matrices of operator norm at most one to a collection of commuting self-adjoint contraction operators on a Hilbert space.

Algebraic and Analytic Aspects of Integrable Systems and Painleve Equations

Algebraic and Analytic Aspects of Integrable Systems and Painleve Equations
Author :
Publisher : American Mathematical Soc.
Total Pages : 210
Release :
ISBN-10 : 9781470416546
ISBN-13 : 1470416549
Rating : 4/5 (46 Downloads)

Synopsis Algebraic and Analytic Aspects of Integrable Systems and Painleve Equations by : Anton Dzhamay

This volume contains the proceedings of the AMS Special Session on Algebraic and Analytic Aspects of Integrable Systems and Painlevé Equations, held on January 18, 2014, at the Joint Mathematics Meetings in Baltimore, MD. The theory of integrable systems has been at the forefront of some of the most important developments in mathematical physics in the last 50 years. The techniques to study such systems have solid foundations in algebraic geometry, differential geometry, and group representation theory. Many important special solutions of continuous and discrete integrable systems can be written in terms of special functions such as hypergeometric and basic hypergeometric functions. The analytic tools developed to study integrable systems have numerous applications in random matrix theory, statistical mechanics and quantum gravity. One of the most exciting recent developments has been the emergence of good and interesting discrete and quantum analogues of classical integrable differential equations, such as the Painlevé equations and soliton equations. Many algebraic and analytic ideas developed in the continuous case generalize in a beautifully natural manner to discrete integrable systems. The editors have sought to bring together a collection of expository and research articles that represent a good cross section of ideas and methods in these active areas of research within integrable systems and their applications.

Trends in Number Theory

Trends in Number Theory
Author :
Publisher : American Mathematical Soc.
Total Pages : 258
Release :
ISBN-10 : 9780821898581
ISBN-13 : 0821898582
Rating : 4/5 (81 Downloads)

Synopsis Trends in Number Theory by : Fernando Chamizo

This volume contains the proceedings of the Fifth Spanish Meeting on Number Theory, held from July 8-12, 2013, at the Universidad de Sevilla, Sevilla, Spain. The articles contained in this book give a panoramic vision of the current research in number theory, both in Spain and abroad. Some of the topics covered in this volume are classical algebraic number theory, arithmetic geometry, and analytic number theory. This book is published in cooperation with Real Sociedad Matemática Española (RSME).

Trends in Harmonic Analysis and Its Applications

Trends in Harmonic Analysis and Its Applications
Author :
Publisher : American Mathematical Soc.
Total Pages : 218
Release :
ISBN-10 : 9781470418793
ISBN-13 : 1470418797
Rating : 4/5 (93 Downloads)

Synopsis Trends in Harmonic Analysis and Its Applications by : Jens G. Christensen

This volume contains the proceedings of the AMS Special Session on Harmonic Analysis and Its Applications held March 29-30, 2014, at the University of Maryland, Baltimore County, Baltimore, MD. It provides an in depth look at the many directions taken by experts in Harmonic Analysis and related areas. The papers cover topics such as frame theory, Gabor analysis, interpolation and Besov spaces on compact manifolds, Cuntz-Krieger algebras, reproducing kernel spaces, solenoids, hypergeometric shift operators and analysis on infinite dimensional groups. Expositions are by leading researchers in the field, both young and established. The papers consist of new results or new approaches to solutions, and at the same time provide an introduction into the respective subjects.

Hodge Theory and Classical Algebraic Geometry

Hodge Theory and Classical Algebraic Geometry
Author :
Publisher : American Mathematical Soc.
Total Pages : 148
Release :
ISBN-10 : 9781470409906
ISBN-13 : 1470409909
Rating : 4/5 (06 Downloads)

Synopsis Hodge Theory and Classical Algebraic Geometry by : Gary Kennedy

This volume contains the proceedings of a conference on Hodge Theory and Classical Algebraic Geometry, held May 13-15, 2013, at The Ohio State University, Columbus, OH. Hodge theory is a powerful tool for the study and classification of algebraic varieties. This volume surveys recent progress in Hodge theory, its generalizations, and applications. The topics range from more classical aspects of Hodge theory to modern developments in compactifications of period domains, applications of Saito's theory of mixed Hodge modules, and connections with derived category theory and non-commutative motives.

Geometry and Topology of Submanifolds and Currents

Geometry and Topology of Submanifolds and Currents
Author :
Publisher : American Mathematical Soc.
Total Pages : 200
Release :
ISBN-10 : 9781470415563
ISBN-13 : 1470415569
Rating : 4/5 (63 Downloads)

Synopsis Geometry and Topology of Submanifolds and Currents by : Weiping Li

he papers in this volume are mainly from the 2013 Midwest Geometry Conference, held October 19, 2013, at Oklahoma State University, Stillwater, OK, and partly from the 2012 Midwest Geometry Conference, held May 12-13, 2012, at the University of Oklahoma, Norman, OK. The papers cover recent results on geometry and topology of submanifolds. On the topology side, topics include Plateau problems, Voevodsky's motivic cohomology, Reidemeister zeta function and systolic inequality, and freedom in 2- and 3-dimensional manifolds. On the geometry side, the authors discuss classifying isoparametric hypersurfaces and review Hartogs triangle, finite volume flows, nonexistence of stable p-currents, and a generalized Bernstein type problem. The authors also show that the interaction between topology and geometry is a key to deeply understanding topological invariants and the geometric problems.

Analysis, Probability And Mathematical Physics On Fractals

Analysis, Probability And Mathematical Physics On Fractals
Author :
Publisher : World Scientific
Total Pages : 594
Release :
ISBN-10 : 9789811215544
ISBN-13 : 9811215545
Rating : 4/5 (44 Downloads)

Synopsis Analysis, Probability And Mathematical Physics On Fractals by : Patricia Alonso Ruiz

In the 50 years since Mandelbrot identified the fractality of coastlines, mathematicians and physicists have developed a rich and beautiful theory describing the interplay between analytic, geometric and probabilistic aspects of the mathematics of fractals. Using classical and abstract analytic tools developed by Cantor, Hausdorff, and Sierpinski, they have sought to address fundamental questions: How can we measure the size of a fractal set? How do waves and heat travel on irregular structures? How are analysis, geometry and stochastic processes related in the absence of Euclidean smooth structure? What new physical phenomena arise in the fractal-like settings that are ubiquitous in nature?This book introduces background and recent progress on these problems, from both established leaders in the field and early career researchers. The book gives a broad introduction to several foundational techniques in fractal mathematics, while also introducing some specific new and significant results of interest to experts, such as that waves have infinite propagation speed on fractals. It contains sufficient introductory material that it can be read by new researchers or researchers from other areas who want to learn about fractal methods and results.

Algorithmic Problems of Group Theory, Their Complexity, and Applications to Cryptography

Algorithmic Problems of Group Theory, Their Complexity, and Applications to Cryptography
Author :
Publisher : American Mathematical Soc.
Total Pages : 136
Release :
ISBN-10 : 9780821898598
ISBN-13 : 0821898590
Rating : 4/5 (98 Downloads)

Synopsis Algorithmic Problems of Group Theory, Their Complexity, and Applications to Cryptography by : Delaram Kahrobaei

This volume contains the proceedings of the AMS Special Session on Algorithmic Problems of Group Theory and Their Complexity, held January 9-10, 2013 in San Diego, CA and the AMS Special Session on Algorithmic Problems of Group Theory and Applications to Information Security, held April 6-7, 2013 at Boston College, Chestnut Hill, MA. Over the past few years the field of group-based cryptography has attracted attention from both group theorists and cryptographers. The new techniques inspired by algorithmic problems in non-commutative group theory and their complexity have offered promising ideas for developing new cryptographic protocols. The papers in this volume cover algorithmic group theory and applications to cryptography.