This book unites descriptive set theory and definable proper forcing and explores the relations between them. Both forcing and descriptive set theory are explained independently, their sub-areas described, following their commitment to each other. Containing original research, this text highlights the connections that forcing makes with other areas of mathematics, and is essential reading for academic researchers and graduate students in set theory, abstract analysis, and measure theory.
This book unites descriptive set theory and definable proper forcing and explores the relations between them. Both forcing and descriptive set theory ...
Eleven of the fourteen invited speakers at a symposium held by the Oxford Mathematical Institute in 1972 have submitted their contributions for publication in this volume.
Eleven of the fourteen invited speakers at a symposium held by the Oxford Mathematical Institute in 1972 have submitted their contributions for public...
The dynamics of linear operators is a young and rapidly evolving branch of functional analysis. In this book, which focuses on hypercyclicity and supercyclicity, the authors assemble the wide body of theory that has received much attention over the last fifteen years and present it for the first time in book form. Selected topics include various kinds of existence theorems, the role of connectedness in hypercyclicity, linear dynamics and ergodic theory, frequently hypercyclic and chaotic operators, hypercyclic subspaces, the angle criterion, universality of the Riemann zeta function, and an...
The dynamics of linear operators is a young and rapidly evolving branch of functional analysis. In this book, which focuses on hypercyclicity and supe...
Totally positive matrices constitute a particular class of matrices, the study of which was initiated by analysts because of its many applications in diverse areas. This account of the subject is comprehensive and thorough, with careful treatment of the central properties of totally positive matrices, full proofs and a complete bibliography. The history of the subject is also described: in particular, the book ends with a tribute to the four people who have made the most notable contributions to the history of total positivity: I. J. Schoenberg, M. G. Krein, F. R. Gantmacher and S. Karlin....
Totally positive matrices constitute a particular class of matrices, the study of which was initiated by analysts because of its many applications in ...
Many classical results of geometric function theory extend to harmonic mappings, but basic questions remain unresolved. This book is the first comprehensive account of the theory of planar harmonic mappings, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces. It contains background material in complex analysis and a full development of the classical theory of minimal surfaces, including the Weierstrass-Enneper representation. It introduces non-specialists to a beautiful area of complex analysis and geometry.
Many classical results of geometric function theory extend to harmonic mappings, but basic questions remain unresolved. This book is the first compreh...
This accessible research monograph investigates how 'finite-dimensional' sets can be embedded into finite-dimensional Euclidean spaces. The first part brings together a number of abstract embedding results, and provides a unified treatment of four definitions of dimension that arise in disparate fields: Lebesgue covering dimension (from classical 'dimension theory'), Hausdorff dimension (from geometric measure theory), upper box-counting dimension (from dynamical systems), and Assouad dimension (from the theory of metric spaces). These abstract embedding results are applied in the second part...
This accessible research monograph investigates how 'finite-dimensional' sets can be embedded into finite-dimensional Euclidean spaces. The first part...
This self-contained monograph presents rigidity theory for a large class of dynamical systems, differentiable higher rank hyperbolic and partially hyperbolic actions. This first volume describes the subject in detail and develops the principal methods presently used in various aspects of the rigidity theory. Part I serves as an exposition and preparation, including a large collection of examples that are difficult to find in the existing literature. Part II focuses on cocycle rigidity, which serves as a model for rigidity phenomena as well as a useful tool for studying them. The book is an...
This self-contained monograph presents rigidity theory for a large class of dynamical systems, differentiable higher rank hyperbolic and partially hyp...