Series: The IMA Volumes in Mathematics and its Applications , Vol. 149
2008, Approx. 375 p., Hardcover
ISBN: 978-0-387-09685-8
Due: September 2008
Recent advances in both the theory and implementation of computational algebraic geometry have led to new, striking applications to a variety of fields of research.
The articles in this volume highlight a range of these applications and provide introductory material for topics covered in the IMA workshops on "Optimization and Control" and "Applications in Biology, Dynamics, and Statistics" held during the IMA year on Applications of Algebraic Geometry. The articles related to optimization and control focus on burgeoning use of semidefinite programming and moment matrix techniques in computational real algebraic geometry. The new direction towards a systematic study of non-commutative real algebraic geometry is well represented in the volume. Other articles provide an overview of the way computational algebra is useful for analysis of contingency tables, reconstruction of phylogenetic trees, and in systems biology. The contributions collected in this volume are accessible to non-experts, self-contained and informative; they quickly move towards cutting edge research in these areas, and provide a wealth of open problems for future research.
Foreword.- Preface.- Polynomial optimization on odd-dimensional spheres.- Engineering systems and free semi-algebraic geometry.- Algebraic statistics and contingency table problems: Log-linear models, likelihood estimation, and disclosure limitation.- Using invariants for phylogenetic tree construction.- On the algebraic geometry of polynomial dynamical systems.- A unified approach to computing real and complex zeros of zero-dimensional ideals.- Sums of squares, moment matrices and optimization over polynomials.- Positivity and sums of squares: A guide to recent results.- Noncommutative real algebraic geometry some basic concepts and first ideas.- Open problems in algebraic statistics.- List of workshop participants.-
Series: Graduate Texts in Mathematics , Preliminary entry 249
Originally published by Prentice Hall
2nd ed., 2008, Approx. 505 p. 10 illus., Hardcover
ISBN: 978-0-387-09431-1
Due: October 2008
Historical notes at the end of each chapter
Numerous exercises for each chapter
User-friendly exposition with examples illustrating the definitions and ideas
The primary goal of these two volumes is to present the theoretical foundation of the field of Euclidean Harmonic analysis. The original edition was published as a single volume, but due to its size, scope, and the addition of new material, the second edition consists of two volumes. The present edition contains a new chapter on time-frequency analysis and the Carleson-Hunt theorem. The first volume contains the classical topics such as Interpolation, Fourier Series, the Fourier Transform, Maximal Functions, Singular Integrals, and Littlewood-Paley Theory. The second volume contains more recent topics such as Function Spaces, Atomic Decompositions, Singular Integrals of Nonconvolution Type, and Weighted Inequalities.
These volumes are mainly addressed to graduate students in mathematics and are designed for a two-course sequence on the subject with additional material included for reference. The prerequisites for the first volume are satisfactory completion of courses in real and complex variables. The second volume assumes material from the first. This book is intended to present the selected topics in depth and stimulate further study. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the fundamentals of analysis on the torus. This material is included for historical reasons, as the genesis of Fourier analysis can be found in trigonometric expansions of periodic functions in several variables.
Preface.- Lp Spaces and Interpolation.- Maximal Functions, Fourier Transform, and Distributions.- Fourier Analysis on the Torus.- Singular Integrals of Convolution Type.- Littlewood-Paley Theory and Multipliers.- Gamma and Beta Functions.- Bessel Functions.- Rademacher Functions.- Spherical Coordinates.- Some Trigonometric Identities and Inequalities.- Summation by Parts.- Basic Functional Analysis.- The Minimax Lemma.- The Schur Lemma.- The Whitney Decomposition of Open Sets in Rn.- Smoothness and Vanishing Moments.- Glossary.- References.- Index.
Series: Graduate Texts in Mathematics , Preliminary entry 250
Originally published by Prentice Hall
2nd ed., 2008, Approx. 700 p. 27 illus., Hardcover
ISBN: 978-0-387-09433-5
Due: September 2008
Historical notes at the end of each chapter
Numerous exercises for each chapter
User-friendly exposition with examples illustrating the definitions and ideas
The primary goal of this text is to present the theoretical foundation of the field of Fourier analysis. This book is mainly addressed to graduate students in mathematics and is designed to serve for a three-course sequence on the subject. The only prerequisite for understanding the text is satisfactory completion of a course in measure theory, Lebesgue integration, and complex variables. This book is intended to present the selected topics in some depth and stimulate further study. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the fundamentals of analysis on the torus. This material is included for historical reasons, as the genesis of Fourier analysis can be found in trigonometric expansions of periodic functions in several variables.
While the 1st edition was published as a single volume, the new edition will contain 120 pp of new material, with an additional chaper on time-frequency analysis and other modern topics. As a result, the book is now being published in 2 separate volumes, the first volume containing the classical topics (Lp Spaces, Littlewood-Paley Theory, Smoothness, etc...), the second volume containing the modern topics (weighted inequalities, wavelets, atomic decomposition, etc...).
“Grafakos’s book is very user-friendly with numerous examples illustrating the definitions and ideas. It is more suitable for readers who want to get a feel for current research. The treatment is thoroughly modern with free use of operators and functional analysis. Morever, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises.” - Ken Ross, MAA Online
Preface.- BMO and Carleson Measures.- Singular Integrals of Nonconvolution Type.- Weighted Inequalities.- Boundedness and Convergence of Fourier Integrals.- Appendix A: Gamma and Beta Functions.- Appendix B: Bessel Functions.- Appendix C: Rademacher Functions.- Appendix D: Spherical Coordinates.- Appendix E: Some Trigonometric Identities and Inequalities.- Appendix F: Summation by Parts.- Basic Functional Analysis.- Appendix H: The Minimax Lemma.- Appendix I: The Schur Lemma.- Appendix J: The Whitney Decomposition of Open Sets in Rn.- Appendix K: Smoothness and Vanishing Moments.- Bibliography.- Index of Notation.- Index.
Series: Birkhauser Advanced Texts / Basler Lehrbucher
2009, Approx. 340 p., Hardcover
ISBN: 978-3-7643-8885-0
Due: October 2008
Provides a well-organized account of the asymptotic behavior of subharmonic functions (in n dimensions) with applications to the study of the growth of entire functions of one complex variable
Clearly written, at the level of a second year graduate student specializing in analysis, and contains many exercises
Presents the application of a new tool, the limit set of entire and subharmonic functions
In this book an account of the growth theory of subharmonic functions is given, which is directed towards its applications to entire functions of one and several complex variables.
The presentation aims at converting the noble art of constructing an entire function with prescribed asymptotic behaviour to a handicraft. For this one should only construct the limit set that describes the asymptotic behaviour of the entire function.
All necessary material is developed within the book, hence it will be most useful as a reference book for the construction of entire functions.
1. Preface.- 2. Auxiliary information. Subharmonic functions.- 3. Asymptotic behavior of subharmonic functions of finite order.- 4. Structure of the limit sets.- 5. Applications to entire functions.- 6. Application to the completeness of exponential systems in a convex domain and the multiplicator problem.- Notation.- List of terms.- References.
Series: Undergraduate Texts in Mathematics
2008, 165 illus., Hardcover
ISBN: 978-0-387-79710-6
Due: September 2008
Includes useful pointers to further reading at the post-graduate level
Definitions are followed by representative examples
contains numerous exercises, figures, and exposition
More streamlined than most similar texts
This book covers a wide variety of topics in combinatorics and graph theory. It includes results and problems that cross subdisciplines, emphasizing relationships between different areas of mathematics. In addition, recent results appear in the text, illustrating the fact that mathematics is a living discipline.
The second edition includes many new topics and features:
* New sections in graph theory on distance, Eulerian trails, and Hamiltonian
paths.
* New material on partitions, multinomial coefficients, and the pigeonhole
principle.
* Expanded coverage of Polya Theory to include de Bruijn’s method for
counting arrangements when a second symmetry group acts on the set of allowed
colors.
* Topics in combinatorial geometry, including Erdos and Szekeres’ development
of Ramsey Theory in a problem about convex polygons determined by sets
of points.
* Expanded coverage of stable marriage problems, and new sections on marriage
problems for infinite sets, both countable and uncountable.
* Numerous new exercises throughout the book.
Preface to the second edition.- Preface.- Graph theory.- Combinatorics.- Infinite combinatorics and graphs.- References.- Index.