H[p Superscript] Spaces of an Annulus
Author | : Donald Sarason |
Publisher | : |
Total Pages | : 94 |
Release | : 1965 |
Genre | : Hilbert space |
ISBN | : |
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Author | : Donald Sarason |
Publisher | : |
Total Pages | : 94 |
Release | : 1965 |
Genre | : Hilbert space |
ISBN | : |
Author | : Donald Sarason |
Publisher | : |
Total Pages | : 78 |
Release | : 1965 |
Genre | : Automorphic functions |
ISBN | : |
This paper consists of two parts. The first part is concerned with the basic properties of [italic capital]H[superscript italic]p spaces of a circular annulus, and is function theoretic in character. The second part is an investigation of the invariant subspaces of certain Hilbert space operators, and is functional analytic in character. The questions considered in Part II provided the original motivation for the study that occupies Part I.
Author | : |
Publisher | : Academic Press |
Total Pages | : 277 |
Release | : 1970-07-31 |
Genre | : Mathematics |
ISBN | : 0080873510 |
The theory of HP spaces has its origins in discoveries made forty or fifty years ago by such mathematicians as G. H. Hardy, J. E. Littlewood, I. I. Privalov, F. and M. Riesz, V. Smirnov, and G. Szego. Most of this early work is concerned with the properties of individual functions of class HP, and is classical in spirit. In recent years, the development of functional analysis has stimulated new interest in the HP classes as linear spaces. This point of viewhas suggested a variety of natural problems and has provided new methods of attack, leading to important advances in the theory. This book is an account of both aspects of the subject, the classical and the modern. It is intended to provide a convenient source for the older parts of the theory (the work of Hardy and Littlewood, for example), as well as to give a self-contained exposition of more recent developments such as Beurling’s theorem on invariant subspaces, the Macintyre-RogosinskiShapiro-Havinson theory of extremal problems, interpolation theory, the dual space structure of HP with p
Author | : F. R. Cohen |
Publisher | : Springer |
Total Pages | : 501 |
Release | : 2007-01-05 |
Genre | : Mathematics |
ISBN | : 3540379851 |
Author | : Chris Wendl |
Publisher | : Springer |
Total Pages | : 294 |
Release | : 2018-06-28 |
Genre | : Mathematics |
ISBN | : 3319913719 |
This monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three. The first half of the book focuses on McDuff's characterization of symplectic rational and ruled surfaces, one of the classic early applications of holomorphic curve theory. The proof presented here uses the language of Lefschetz fibrations and pencils, thus it includes some background on these topics, in addition to a survey of the required analytical results on holomorphic curves. Emphasizing applications rather than technical results, the analytical survey mostly refers to other sources for proofs, while aiming to provide precise statements that are widely applicable, plus some informal discussion of the analytical ideas behind them. The second half of the book then extends this program in two complementary directions: (1) a gentle introduction to Gromov-Witten theory and complete proof of the classification of uniruled symplectic 4-manifolds; and (2) a survey of punctured holomorphic curves and their applications to questions from 3-dimensional contact topology, such as classifying the symplectic fillings of planar contact manifolds. This book will be particularly useful to graduate students and researchers who have basic literacy in symplectic geometry and algebraic topology, and would like to learn how to apply standard techniques from holomorphic curve theory without dwelling more than necessary on the analytical details. This book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019
Author | : Danny Calegari |
Publisher | : Oxford University Press on Demand |
Total Pages | : 378 |
Release | : 2007-05-17 |
Genre | : Mathematics |
ISBN | : 0198570082 |
This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.
Author | : Shmuel Weinberger |
Publisher | : University of Chicago Press |
Total Pages | : 314 |
Release | : 1994 |
Genre | : Mathematics |
ISBN | : 9780226885667 |
This book provides the theory for stratified spaces, along with important examples and applications, that is analogous to the surgery theory for manifolds. In the first expository account of this field, Weinberger provides topologists with a new way of looking at the classification theory of singular spaces with his original results. Divided into three parts, the book begins with an overview of modern high-dimensional manifold theory. Rather than including complete proofs of all theorems, Weinberger demonstrates key constructions, gives convenient formulations, and shows the usefulness of the technology. Part II offers the parallel theory for stratified spaces. Here, the topological category is most completely developed using the methods of "controlled topology." Many examples illustrating the topological invariance and noninvariance of obstructions and characteristic classes are provided. Applications for embeddings and immersions of manifolds, for the geometry of group actions, for algebraic varieties, and for rigidity theorems are found in Part III. This volume will be of interest to topologists, as well as mathematicians in other fields such as differential geometry, operator theory, and algebraic geometry.
Author | : Haynes R Miller |
Publisher | : World Scientific |
Total Pages | : 405 |
Release | : 2021-09-20 |
Genre | : Mathematics |
ISBN | : 9811231265 |
Algebraic Topology and basic homotopy theory form a fundamental building block for much of modern mathematics. These lecture notes represent a culmination of many years of leading a two-semester course in this subject at MIT. The style is engaging and student-friendly, but precise. Every lecture is accompanied by exercises. It begins slowly in order to gather up students with a variety of backgrounds, but gains pace as the course progresses, and by the end the student has a command of all the basic techniques of classical homotopy theory.
Author | : Herbert Edelsbrunner |
Publisher | : American Mathematical Society |
Total Pages | : 241 |
Release | : 2022-01-31 |
Genre | : Mathematics |
ISBN | : 1470467690 |
Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering. The main approach is the discovery of topology through algorithms. The book is ideal for teaching a graduate or advanced undergraduate course in computational topology, as it develops all the background of both the mathematical and algorithmic aspects of the subject from first principles. Thus the text could serve equally well in a course taught in a mathematics department or computer science department.
Author | : Steve Y. Oudot |
Publisher | : American Mathematical Soc. |
Total Pages | : 229 |
Release | : 2017-05-17 |
Genre | : Mathematics |
ISBN | : 1470434431 |
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.