Foundations Of Free Noncommutative Function Theory

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Foundations of Free Noncommutative Function Theory

Dmitry S. Kaliuzhnyi-Verbovetskyi,Victor Vinnikov
Foundations of Free Noncommutative Function Theory Book PDF

Author : Dmitry S. Kaliuzhnyi-Verbovetskyi,Victor Vinnikov
Publisher : American Mathematical Soc.
Page : 194 pages
File Size : 54,8 Mb
Release : 2014-11-19
Category : Mathematics
ISBN : 9781470416973

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Foundations of Free Noncommutative Function Theory by Dmitry S. Kaliuzhnyi-Verbovetskyi,Victor Vinnikov Pdf

In this book the authors develop a theory of free noncommutative functions, in both algebraic and analytic settings. Such functions are defined as mappings from square matrices of all sizes over a module (in particular, a vector space) to square matrices over another module, which respect the size, direct sums, and similarities of matrices. Examples include, but are not limited to, noncommutative polynomials, power series, and rational expressions. Motivation and inspiration for using the theory of free noncommutative functions often comes from free probability. An important application area is "dimensionless" matrix inequalities; these arise, e.g., in various optimization problems of system engineering. Among other related areas are those of polynomial identities in rings, formal languages and finite automata, quasideterminants, noncommutative symmetric functions, operator spaces and operator algebras, and quantum control.

Multivariable Operator Theory

Ernst Albrecht,Raúl Curto,Michael Hartz,Mihai Putinar
Multivariable Operator Theory Book PDF

Author : Ernst Albrecht,Raúl Curto,Michael Hartz,Mihai Putinar
Publisher : Springer Nature
Page : 893 pages
File Size : 46,6 Mb
Release : 2024-01-22
Category : Mathematics
ISBN : 9783031505355

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Multivariable Operator Theory by Ernst Albrecht,Raúl Curto,Michael Hartz,Mihai Putinar Pdf

Over the course of his distinguished career, Jörg Eschmeier made a number of fundamental contributions to the development of operator theory and related topics. The chapters in this volume, compiled in his memory, are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.

Realization and Model Reduction of Dynamical Systems

Christopher Beattie,Peter Benner,Mark Embree,Serkan Gugercin,Sanda Lefteriu
Realization and Model Reduction of Dynamical Systems Book PDF

Author : Christopher Beattie,Peter Benner,Mark Embree,Serkan Gugercin,Sanda Lefteriu
Publisher : Springer Nature
Page : 462 pages
File Size : 44,5 Mb
Release : 2022-06-09
Category : Science
ISBN : 9783030951573

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Realization and Model Reduction of Dynamical Systems by Christopher Beattie,Peter Benner,Mark Embree,Serkan Gugercin,Sanda Lefteriu Pdf

This book celebrates Professor Thanos Antoulas's 70th birthday, marking his fundamental contributions to systems and control theory, especially model reduction and, more recently, data-driven modeling and system identification. Model reduction is a prominent research topic with wide ranging scientific and engineering applications.

Random Matrices

Alexei Borodin,Ivan Corwin,Alice Guionnet
Random Matrices Book PDF

Author : Alexei Borodin,Ivan Corwin,Alice Guionnet
Publisher : American Mathematical Soc.
Page : 498 pages
File Size : 44,6 Mb
Release : 2019-10-30
Category : Education
ISBN : 9781470452803

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Random Matrices by Alexei Borodin,Ivan Corwin,Alice Guionnet Pdf

Random matrix theory has many roots and many branches in mathematics, statistics, physics, computer science, data science, numerical analysis, biology, ecology, engineering, and operations research. This book provides a snippet of this vast domain of study, with a particular focus on the notations of universality and integrability. Universality shows that many systems behave the same way in their large scale limit, while integrability provides a route to describe the nature of those universal limits. Many of the ten contributed chapters address these themes, while others touch on applications of tools and results from random matrix theory. This book is appropriate for graduate students and researchers interested in learning techniques and results in random matrix theory from different perspectives and viewpoints. It also captures a moment in the evolution of the theory, when the previous decade brought major break-throughs, prompting exciting new directions of research.

Computation and Combinatorics in Dynamics, Stochastics and Control

Elena Celledoni,Giulia Di Nunno,Kurusch Ebrahimi-Fard,Hans Zanna Munthe-Kaas
Computation and Combinatorics in Dynamics Stochastics and Control Book PDF

Author : Elena Celledoni,Giulia Di Nunno,Kurusch Ebrahimi-Fard,Hans Zanna Munthe-Kaas
Publisher : Springer
Page : 734 pages
File Size : 46,6 Mb
Release : 2019-01-13
Category : Mathematics
ISBN : 9783030015930

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Computation and Combinatorics in Dynamics, Stochastics and Control by Elena Celledoni,Giulia Di Nunno,Kurusch Ebrahimi-Fard,Hans Zanna Munthe-Kaas Pdf

The Abel Symposia volume at hand contains a collection of high-quality articles written by the world’s leading experts, and addressing all mathematicians interested in advances in deterministic and stochastic dynamical systems, numerical analysis, and control theory. In recent years we have witnessed a remarkable convergence between individual mathematical disciplines that approach deterministic and stochastic dynamical systems from mathematical analysis, computational mathematics and control theoretical perspectives. Breakthrough developments in these fields now provide a common mathematical framework for attacking many different problems related to differential geometry, analysis and algorithms for stochastic and deterministic dynamics. In the Abel Symposium 2016, which took place from August 16-19 in Rosendal near Bergen, leading researchers in the fields of deterministic and stochastic differential equations, control theory, numerical analysis, algebra and random processes presented and discussed the current state of the art in these diverse fields. The current Abel Symposia volume may serve as a point of departure for exploring these related but diverse fields of research, as well as an indicator of important current and future developments in modern mathematics.

Interpolation and Realization Theory with Applications to Control Theory

Vladimir Bolotnikov,Sanne ter Horst,André C.M. Ran,Victor Vinnikov
Interpolation and Realization Theory with Applications to Control Theory Book PDF

Author : Vladimir Bolotnikov,Sanne ter Horst,André C.M. Ran,Victor Vinnikov
Publisher : Springer
Page : 353 pages
File Size : 48,9 Mb
Release : 2019-04-08
Category : Mathematics
ISBN : 9783030116149

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Interpolation and Realization Theory with Applications to Control Theory by Vladimir Bolotnikov,Sanne ter Horst,André C.M. Ran,Victor Vinnikov Pdf

This volume is devoted to Joseph A. (Joe) Ball’s contributions to operator theory and its applications and in celebration of his seventieth birthday. Joe Ball’s career spans over four and a half decades, starting with his work on model theory and related topics for non-contractions and operators on multiply connected domains. Later on, more applied operator theory themes appeared in his work, involving factorization and interpolation for operator-valued functions, with extensive applications in system and control theory. He has worked on nonlinear control, time-varying systems and, more recently, on multidimensional systems and noncommutative H∞-theory on the unit ball and polydisk, and more general domains, and these are only the main themes in his vast oeuvre. Fourteen research papers constitute the core of this volume, written by mathematicians who have collaborated with Joe or have been influenced by his vast mathematical work. A curriculum vitae, a publications list and a list of Joe Ball’s PhD students are included in this volume, as well as personal reminiscences by colleagues and friends. Contributions by Yu. M. Arlinskii, S. Hassi, M. Augat, J. W. Helton, I. Klep, S. McCullough, S. Balasubramanian, U. Wijesooriya, N. Cohen, Q. Fang, S. Gorai, J. Sarkar, G. J. Groenewald, S. ter Horst, J. Jaftha, A. C. M. Ran, M.A. Kaashoek, F. van Schagen, A. Kheifets, Z. A. Lykova, N. J. Young, A. E. Ajibo, R. T. W. Martin, A. Ramanantoanina, M.-J. Y. Ou, H. J. Woerdeman, A. van der Schaft, A. Tannenbaum, T. T. Georgiou, J. O. Deasy and L. Norton.

Foundations of Arithmetic Differential Geometry

Alexandru Buium
Foundations of Arithmetic Differential Geometry Book PDF

Author : Alexandru Buium
Publisher : American Mathematical Society
Page : 357 pages
File Size : 40,9 Mb
Release : 2023-11-20
Category : Mathematics
ISBN : 9781470475772

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Foundations of Arithmetic Differential Geometry by Alexandru Buium Pdf

The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is “intrinsically curved”; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.

Operator Analysis

Jim Agler,John Edward McCarthy,Nicholas John Young
Operator Analysis Book PDF

Author : Jim Agler,John Edward McCarthy,Nicholas John Young
Publisher : Cambridge University Press
Page : 393 pages
File Size : 47,5 Mb
Release : 2020-03-26
Category : Mathematics
ISBN : 9781108485449

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Operator Analysis by Jim Agler,John Edward McCarthy,Nicholas John Young Pdf

This monograph, aimed at graduate students and researchers, explores the use of Hilbert space methods in function theory. Explaining how operator theory interacts with function theory in one and several variables, the authors journey from an accessible explanation of the techniques to their uses in cutting edge research.

Persistence Theory: From Quiver Representations to Data Analysis

Steve Y. Oudot
Persistence Theory From Quiver Representations to Data Analysis Book PDF

Author : Steve Y. Oudot
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 48,8 Mb
Release : 2017-05-17
Category : Electronic
ISBN : 9781470434434

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Persistence Theory: From Quiver Representations to Data Analysis by Steve Y. Oudot Pdf

Persistence theory emerged in the early 2000s as a new theory in the area of applied and computational topology. This book provides a broad and modern view of the subject, including its algebraic, topological, and algorithmic aspects. It also elaborates on applications in data analysis. The level of detail of the exposition has been set so as to keep a survey style, while providing sufficient insights into the proofs so the reader can understand the mechanisms at work. The book is organized into three parts. The first part is dedicated to the foundations of persistence and emphasizes its connection to quiver representation theory. The second part focuses on its connection to applications through a few selected topics. The third part provides perspectives for both the theory and its applications. The book can be used as a text for a course on applied topology or data analysis.

Optimization of Polynomials in Non-Commuting Variables

Sabine Burgdorf,Igor Klep,Janez Povh
Optimization of Polynomials in Non Commuting Variables Book PDF

Author : Sabine Burgdorf,Igor Klep,Janez Povh
Publisher : Springer
Page : 118 pages
File Size : 51,8 Mb
Release : 2016-06-07
Category : Mathematics
ISBN : 9783319333380

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Optimization of Polynomials in Non-Commuting Variables by Sabine Burgdorf,Igor Klep,Janez Povh Pdf

This book presents recent results on positivity and optimization of polynomials in non-commuting variables. Researchers in non-commutative algebraic geometry, control theory, system engineering, optimization, quantum physics and information science will find the unified notation and mixture of algebraic geometry and mathematical programming useful. Theoretical results are matched with algorithmic considerations; several examples and information on how to use NCSOStools open source package to obtain the results provided. Results are presented on detecting the eigenvalue and trace positivity of polynomials in non-commuting variables using Newton chip method and Newton cyclic chip method, relaxations for constrained and unconstrained optimization problems, semidefinite programming formulations of the relaxations and finite convergence of the hierarchies of these relaxations, and the practical efficiency of algorithms.

Grid Homology for Knots and Links

Peter S. Ozsváth,András I. Stipsicz,Zoltán Szabó
Grid Homology for Knots and Links Book PDF

Author : Peter S. Ozsváth,András I. Stipsicz,Zoltán Szabó
Publisher : American Mathematical Soc.
Page : 410 pages
File Size : 46,9 Mb
Release : 2015-12-04
Category : Homology theory
ISBN : 9781470417376

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Grid Homology for Knots and Links by Peter S. Ozsváth,András I. Stipsicz,Zoltán Szabó Pdf

Knot theory is a classical area of low-dimensional topology, directly connected with the theory of three-manifolds and smooth four-manifold topology. In recent years, the subject has undergone transformative changes thanks to its connections with a number of other mathematical disciplines, including gauge theory; representation theory and categorification; contact geometry; and the theory of pseudo-holomorphic curves. Starting from the combinatorial point of view on knots using their grid diagrams, this book serves as an introduction to knot theory, specifically as it relates to some of the above developments. After a brief overview of the background material in the subject, the book gives a self-contained treatment of knot Floer homology from the point of view of grid diagrams. Applications include computations of the unknotting number and slice genus of torus knots (asked first in the 1960s and settled in the 1990s), and tools to study variants of knot theory in the presence of a contact structure. Additional topics are presented to prepare readers for further study in holomorphic methods in low-dimensional topology, especially Heegaard Floer homology. The book could serve as a textbook for an advanced undergraduate or part of a graduate course in knot theory. Standard background material is sketched in the text and the appendices.

The Ricci Flow: Techniques and Applications

Bennett Chow,Sun-Chin Chu,David Glickenstein,Christine Guenther, James Isenberg,Tom Ivey,Dan Knopf,Peng Lu,Feng Luo,Lei Ni
The Ricci Flow Techniques and Applications Book PDF

Author : Bennett Chow,Sun-Chin Chu,David Glickenstein,Christine Guenther, James Isenberg,Tom Ivey,Dan Knopf,Peng Lu,Feng Luo,Lei Ni
Publisher : American Mathematical Soc.
Page : 374 pages
File Size : 50,8 Mb
Release : 2015-10-19
Category : Electronic
ISBN : 9780821849910

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The Ricci Flow: Techniques and Applications by Bennett Chow,Sun-Chin Chu,David Glickenstein,Christine Guenther, James Isenberg,Tom Ivey,Dan Knopf,Peng Lu,Feng Luo,Lei Ni Pdf

Ricci flow is a powerful technique using a heat-type equation to deform Riemannian metrics on manifolds to better metrics in the search for geometric decompositions. With the fourth part of their volume on techniques and applications of the theory, the authors discuss long-time solutions of the Ricci flow and related topics. In dimension 3, Perelman completed Hamilton's program to prove Thurston's geometrization conjecture. In higher dimensions the Ricci flow has remarkable properties, which indicates its usefulness to understand relations between the geometry and topology of manifolds. This book discusses recent developments on gradient Ricci solitons, which model the singularities developing under the Ricci flow. In the shrinking case there is a surprising rigidity which suggests the likelihood of a well-developed structure theory. A broader class of solutions is ancient solutions; the authors discuss the beautiful classification in dimension 2. In higher dimensions they consider both ancient and singular Type I solutions, which must have shrinking gradient Ricci soliton models. Next, Hamilton's theory of 3-dimensional nonsingular solutions is presented, following his original work. Historically, this theory initially connected the Ricci flow to the geometrization conjecture. From a dynamical point of view, one is interested in the stability of the Ricci flow. The authors discuss what is known about this basic problem. Finally, they consider the degenerate neckpinch singularity from both the numerical and theoretical perspectives. This book makes advanced material accessible to researchers and graduate students who are interested in the Ricci flow and geometric evolution equations and who have a knowledge of the fundamentals of the Ricci flow.

Galois Theories of Linear Difference Equations: An Introduction

Charlotte Hardouin,Jacques Sauloy,Michael F. Singer
Galois Theories of Linear Difference Equations An Introduction Book PDF

Author : Charlotte Hardouin,Jacques Sauloy,Michael F. Singer
Publisher : American Mathematical Soc.
Page : 171 pages
File Size : 48,9 Mb
Release : 2016-04-27
Category : Difference and functional equations -- Difference equations -- Linear equations
ISBN : 9781470426552

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Galois Theories of Linear Difference Equations: An Introduction by Charlotte Hardouin,Jacques Sauloy,Michael F. Singer Pdf

This book is a collection of three introductory tutorials coming out of three courses given at the CIMPA Research School “Galois Theory of Difference Equations” in Santa Marta, Columbia, July 23–August 1, 2012. The aim of these tutorials is to introduce the reader to three Galois theories of linear difference equations and their interrelations. Each of the three articles addresses a different galoisian aspect of linear difference equations. The authors motivate and give elementary examples of the basic ideas and techniques, providing the reader with an entry to current research. In addition each article contains an extensive bibliography that includes recent papers; the authors have provided pointers to these articles allowing the interested reader to explore further.

Geometry and Dynamics in Gromov Hyperbolic Metric Spaces

Tushar Das,David Simmons,Mariusz Urbański
Geometry and Dynamics in Gromov Hyperbolic Metric Spaces Book PDF

Author : Tushar Das,David Simmons,Mariusz Urbański
Publisher : American Mathematical Soc.
Page : 281 pages
File Size : 48,8 Mb
Release : 2017-04-14
Category : Geometry, Hyperbolic
ISBN : 9781470434656

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Geometry and Dynamics in Gromov Hyperbolic Metric Spaces by Tushar Das,David Simmons,Mariusz Urbański Pdf

This book presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Particular emphasis is paid to the geometry of their limit sets and on behavior not found in the proper setting. The authors provide a number of examples of groups which exhibit a wide range of phenomena not to be found in the finite-dimensional theory. The book contains both introductory material to help beginners as well as new research results, and closes with a list of attractive unsolved problems.

Partial Dynamical Systems, Fell Bundles and Applications

Ruy Exel
Partial Dynamical Systems Fell Bundles and Applications Book PDF

Author : Ruy Exel
Publisher : American Mathematical Soc.
Page : 321 pages
File Size : 53,6 Mb
Release : 2017-09-20
Category : Banach spaces
ISBN : 9781470437855

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Partial Dynamical Systems, Fell Bundles and Applications by Ruy Exel Pdf

Partial dynamical systems, originally developed as a tool to study algebras of operators in Hilbert spaces, has recently become an important branch of algebra. Its most powerful results allow for understanding structural properties of algebras, both in the purely algebraic and in the C*-contexts, in terms of the dynamical properties of certain systems which are often hiding behind algebraic structures. The first indication that the study of an algebra using partial dynamical systems may be helpful is the presence of a grading. While the usual theory of graded algebras often requires gradings to be saturated, the theory of partial dynamical systems is especially well suited to treat nonsaturated graded algebras which are in fact the source of the notion of “partiality”. One of the main results of the book states that every graded algebra satisfying suitable conditions may be reconstructed from a partial dynamical system via a process called the partial crossed product. Running in parallel with partial dynamical systems, partial representations of groups are also presented and studied in depth. In addition to presenting main theoretical results, several specific examples are analyzed, including Wiener–Hopf algebras and graph C*-algebras.