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Lectures on Choquet's Theorem

Lectures on Choquet's Theorem
Author: Robert R. Phelps
Publisher: Springer Science & Business Media
Total Pages: 123
Release: 2001-05-08
Genre: Mathematics
ISBN: 3540418342

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A well written, readable and easily accessible introduction to "Choquet theory", which treats the representation of elements of a compact convex set as integral averages over extreme points of the set. The interest in this material arises both from its appealing geometrical nature as well as its extraordinarily wide range of application to areas ranging from approximation theory to ergodic theory. Many of these applications are treated in this book. This second edition is an expanded and updated version of what has become a classic basic reference in the subject.


Lectures on Choquet's Theorem

Lectures on Choquet's Theorem
Author: Robert Ralph Phelps
Publisher:
Total Pages: 144
Release: 1966
Genre: Choquet theory
ISBN:

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Appearing for the first time in book form are the main results centered about Choquet's integral representation theorem-an important recent chapter in functional analysis. This theorem has applications to analysis, probability, potential theory, and functional analysis; it will doubtless have further applications as it becomes better known. This readable book presupposes a knowledge of integration theory and elementary functional analysis, including the Krein-Milman theorem and the Riesz representation theorem. --Back cover.


Lectures on Choquet's Theorem

Lectures on Choquet's Theorem
Author: Robert R. Phelps
Publisher: Springer
Total Pages: 123
Release: 2003-07-01
Genre: Mathematics
ISBN: 3540487190

Download Lectures on Choquet's Theorem Book in PDF, ePub and Kindle

A well written, readable and easily accessible introduction to "Choquet theory", which treats the representation of elements of a compact convex set as integral averages over extreme points of the set. The interest in this material arises both from its appealing geometrical nature as well as its extraordinarily wide range of application to areas ranging from approximation theory to ergodic theory. Many of these applications are treated in this book. This second edition is an expanded and updated version of what has become a classic basic reference in the subject.


Choquet's Theorem and Applications

Choquet's Theorem and Applications
Author: John Edward Parsons
Publisher:
Total Pages: 104
Release: 1975
Genre: Functional analysis
ISBN:

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Lectures On Convex Sets (Second Edition)

Lectures On Convex Sets (Second Edition)
Author: Valeriu Soltan
Publisher: World Scientific
Total Pages: 611
Release: 2019-11-28
Genre: Mathematics
ISBN: 9811202133

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The book provides a self-contained and systematic treatment of algebraic and topological properties of convex sets in the n-dimensional Euclidean space. It benefits advanced undergraduate and graduate students with various majors in mathematics, optimization, and operations research. It may be adapted as a primary book or an additional text for any course in convex geometry or convex analysis, aimed at non-geometers. It can be a source for independent study and a reference book for researchers in academia.The second edition essentially extends and revises the original book. Every chapter is rewritten, with many new theorems, examples, problems, and bibliographical references included. It contains three new chapters and 100 additional problems with solutions.


Lectures on the L2-Sobolev Theory of the [d-bar]-Neumann Problem

Lectures on the L2-Sobolev Theory of the [d-bar]-Neumann Problem
Author: Emil J. Straube
Publisher: European Mathematical Society
Total Pages: 220
Release: 2010
Genre: Mathematics
ISBN: 9783037190760

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This book provides a thorough and self-contained introduction to the $\bar{\partial}$-Neumann problem, leading up to current research, in the context of the $\mathcal{L}^{2}$-Sobolev theory on bounded pseudoconvex domains in $\mathbb{C}^{n}$. It grew out of courses for advanced graduate students and young researchers given by the author at the Erwin Schrodinger International Institute for Mathematical Physics and at Texas A & M University. The introductory chapter provides an overview of the contents and puts them in historical perspective. The second chapter presents the basic $\mathcal{L}^{2}$-theory. Following is a chapter on the subelliptic estimates on strictly pseudoconvex domains. The two final chapters on compactness and on regularity in Sobolev spaces bring the reader to the frontiers of research. Prerequisites are a solid background in basic complex and functional analysis, including the elementary $\mathcal{L}^{2}$-Sobolev theory and distributions. Some knowledge in several complex variables is helpful. Concerning partial differential equations, not much is assumed. The elliptic regularity of the Dirichlet problem for the Laplacian is quoted a few times, but the ellipticity results needed for elliptic regularization in the third chapter are proved from scratch.


Handbook of Dynamical Systems

Handbook of Dynamical Systems
Author: B. Hasselblatt
Publisher: Elsevier
Total Pages: 1231
Release: 2002-08-20
Genre: Mathematics
ISBN: 0080533442

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Volumes 1A and 1B. These volumes give a comprehensive survey of dynamics written by specialists in the various subfields of dynamical systems. The presentation attains coherence through a major introductory survey by the editors that organizes the entire subject, and by ample cross-references between individual surveys. The volumes are a valuable resource for dynamicists seeking to acquaint themselves with other specialties in the field, and to mathematicians active in other branches of mathematics who wish to learn about contemporary ideas and results dynamics. Assuming only general mathematical knowledge the surveys lead the reader towards the current state of research in dynamics. Volume 1B will appear 2005.


Mathematical Epidemiology

Mathematical Epidemiology
Author: Fred Brauer
Publisher: Springer
Total Pages: 415
Release: 2008-04-13
Genre: Medical
ISBN: 3540789111

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Based on lecture notes of two summer schools with a mixed audience from mathematical sciences, epidemiology and public health, this volume offers a comprehensive introduction to basic ideas and techniques in modeling infectious diseases, for the comparison of strategies to plan for an anticipated epidemic or pandemic, and to deal with a disease outbreak in real time. It covers detailed case studies for diseases including pandemic influenza, West Nile virus, and childhood diseases. Models for other diseases including Severe Acute Respiratory Syndrome, fox rabies, and sexually transmitted infections are included as applications. Its chapters are coherent and complementary independent units. In order to accustom students to look at the current literature and to experience different perspectives, no attempt has been made to achieve united writing style or unified notation. Notes on some mathematical background (calculus, matrix algebra, differential equations, and probability) have been prepared and may be downloaded at the web site of the Centre for Disease Modeling (www.cdm.yorku.ca).


Mathematical Models of Granular Matter

Mathematical Models of Granular Matter
Author: Gianfranco Capriz
Publisher: Springer
Total Pages: 228
Release: 2008-04-20
Genre: Technology & Engineering
ISBN: 354078277X

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Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. Prominent directions in the modelling granular flows are analyzed from various points of view. Foundational issues, numerical schemes and experimental results are discussed. The volume furnishes a rather complete overview of the current research trends in the mechanics of granular matter. Various chapters introduce the reader to different points of view and related techniques. New models describing granular bodies as complex bodies are presented. Results on the analysis of the inelastic Boltzmann equations are collected in different chapters. Gallavotti-Cohen symmetry is also discussed.


Algebraic Groups and Lie Groups with Few Factors

Algebraic Groups and Lie Groups with Few Factors
Author: Alfonso Di Bartolo
Publisher: Springer Science & Business Media
Total Pages: 223
Release: 2008-04-17
Genre: Mathematics
ISBN: 3540785833

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This volume treats algebraic groups from a group theoretical point of view and compares the results with the analogous issues in the theory of Lie groups. It examines a classification of algebraic groups and Lie groups having only few subgroups.