Series: Fields Institute Monographs, Vol. 31
2013, VIII, 169 p.
Hardcover version ISBN 978-1-4614-5610-0
Due: December 31, 2012
Includes a comprehensive list of results on integral means taken from several research papers
Text is concise and self-contained, making it easily accessible to graduate students
Provides rapid access to the frontiers of research in this field
Derivatives of Inner Functions was inspired by a conference held at the Fields Institute in 2011 entitled "Blaschke Products and Their Applications." Inner functions form an important subclass of bounded analytic functions. Since they have unimodular boundary values, they appear in many extremal problems of complex analysis. They have been extensively studied since the early twentieth century and the literature on this topic is vast. This book is devoted to a concise study of derivatives of inner functions and is confined to treating the integral means of derivatives and presenting a comprehensive list of results on Hardy and Bergman means.
This self-contained monograph allows researchers to get acquainted with the essentials of inner functions, rendering this theory accessible to graduate students while providing the reader with rapid access to the frontiers of research in this field.
.-Preface.-1. Inner Functions.-2. The Exceptional Set of an Inner Function.-3. The Derivative of Finite Blaschke Products.-4. Angular Derivative.-5. Hp-Means of S'.-6. Bp-Means of S'.-7. The Derivative of a Blaschke Product.-8. Hp-Means of B'.-9. Bp-Means of B'.-10. The Growth of Integral Means of B'.-References.-Index.
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge A Series of Modern Surveys in Mathematics, Vol. 57
2013, 2013, X, 640 p.
Hardcover version ISBN 978-3-642-34452-7
Due: December 2012
A basic reference book on diagram geometry
Treats group theory, matroid theory, Coxeter goups and buildings from a diagrammatic perspective
Graph theorists will find many highly regular graphs
The book contains many examples
This book provides a self-contained introduction to diagram geometry. Tight connections with group theory are shown. It treats thin geometries (related to Coxeter groups) and thick buildings from a diagrammatic perspective. Projective and affine geometry are main examples. Polar geometry is motivated by polarities on diagram geometries and the complete classification of those polar geometries whose projective planes are Desarguesian is given. It differs from Tits' comprehensive treatment in that it uses Veldkamp's embeddings.
The book intends to be a basic reference for those who study diagram geometry. Group theorists will find examples of the use of diagram geometry. Light on matroid theory is shed from the point of view of geometry with linear diagrams. Those interested in Coxeter groups and those interested in buildings will find brief but self-contained introductions into these topics from the diagrammatic perspective. Graph theorists will find many highly regular graphs.
1. Geometries.- 2. Diagrams.- 3. Chamber Systems.- 4. Thin Geometries.- 5. Linear Geometries.- 6. Projective and Affine Spaces.- 7. Polar Spaces.- 8. Projective Embeddings of Polar Spaces.- 9. Embedding Polar Spaces in Absolutes.- 10. Classical Polar Spaces.- 11. Buildings.- Bibliography.- Index.
Series: Lecture Notes in Mathematics, Vol. 2070
2013, XIII, 110 p.
Softcover
ISBN 978-1-4471-4813-5
Due: January 31, 2013
Probabilistic Group Theory, Combinatorics and Computing is based on lecture courses held at the Fifth de Brun Workshop in Galway, Ireland in April 2011. Each course discusses computational and algorithmic aspects that have recently emerged at the interface of group theory and combinatorics, with a strong focus on probabilistic methods and results. The courses served as a forum for devising new strategic approaches and for discussing the main open problems to be solved in the further development of each area. The book represents a valuable resource for advanced lecture courses. Researchers at all levels are introduced to the main methods and the state-of-the-art, leading up to the very latest developments. One primary aim of the book’s approach and design is to enable postgraduate students to make immediate use of the material presented.
Martin W. Liebeck: Probabilistic and asymptotic aspects of finite simple groups.- Alice C. Niemeyer, Cheryl E. Praeger, Akos Seress: Estimation problems and randomised group algorithms.- Leonard H. Soicher: Designs, groups and computing.
Series: Applied and Numerical Harmonic Analysis
2013, X, 316 p.
Hardcover version ISBN 978-3-0348-0547-6
Due: January 31, 2013
Proofs are developed in detail, illustrating the standard techniques used in the field?
Accessible for research mathematicians as well as graduate students
Provides a thorough and up to date bibliographic treatment that makes clear the history and development of the field
This book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They were introduced in the early 1930s but have become the focus of renewed interest since the early 1990s because of their connection with the calculus of variations and partial differential equations with nonstandard growth conditions, and for their applications to problems in physics and image processing.
The book begins with the development of the basic function space properties. It avoids a more abstract, functional analysis approach, instead emphasizing an hands-on approach that makes clear the similarities and differences between the variable and classical Lebesgue spaces. The subsequent chapters are devoted to harmonic analysis on variable Lebesgue spaces. The theory of the Hardy-Littlewood maximal operator is completely developed, and the connections between variable Lebesgue spaces and the weighted norm inequalities are introduced. The other important operators in harmonic analysis - singular integrals, Riesz potentials, and approximate identities - are treated using a powerful generalization of the Rubio de Francia theory of extrapolation from the theory of weighted norm inequalities. The final chapter applies the results from previous chapters to prove basic results about variable Sobolev spaces.?
1 Introduction.- 2 Structure of Variable Lebesgue Spaces.- 3 The Hardy-Littlewood Maximal Operator.- 4 Beyond Log-Holder Continuity.- 5 Extrapolation in the Variable Lebesgue Spaces.- 6 Basic Properties of Variable Sobolev Spaces.- Appendix: Open Problems.- Bibliography.- Symbol Index.- Author Index.- Subject Index. ?
Series: Universitext
2013, 2013, XII, 260 p. 67 illus., 15 in color.
Softcover
ISBN 978-1-4471-4816-6
Due: January 31, 2013
.Provides a mathematical introduction to linear and non-linear (i.e. algebraic) computational geometry
Applies the theory to computer graphics, curve reconstruction and robotics
Establishes interconnections with other disciplines such as algebraic geometry, optimization and numerical mathematics
Polyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. It presents its primary topics from the viewpoints of discrete, convex and elementary algebraic geometry.
The first part of the book studies classical problems and techniques that refer to polyhedral structures. The authors include a study on algorithms for computing convex hulls as well as the construction of Voronoi diagrams and Delone triangulations.
The second part of the book develops the primary concepts of (non-linear) computational algebraic geometry. Here, the book looks at Grobner bases and solving systems of polynomial equations. The theory is illustrated by applications in computer graphics, curve reconstruction and robotics.
Throughout the book, interconnections between computational geometry and other disciplines (such as algebraic geometry, optimization and numerical mathematics) are established.
Polyhedral and Algebraic Methods in Computational Geometry is directed towards advanced undergraduates in mathematics and computer science, as well as towards engineering students who are interested in the applications of computational geometry.
Introduction and Overview.- Geometric Fundamentals.- Polytopes and Polyhedra.- Linear Programming.- Computation of Convex Hulls.- Voronoi Diagrams.- Delone Triangulations.- Algebraic and Geometric Foundations.- Grobner Bases and Buchberger’s Algorithm.- Solving Systems of Polynomial Equations Using Grobner Bases.- Reconstruction of Curves.- Plucker Coordinates and Lines in Space.- Applications of Non-Linear Computational Geometry.- Algebraic Structures.- Separation Theorems.- Algorithms and Complexity.- Software.- Notation.