Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups.
Important revisions to the third edition include:...
Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also conta...
This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Ito's formula, the optional stopping theorem and Girsanov's theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales...
This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuo...
This text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems. The two new chapters in this second edition are devoted to two topics of much current interest amongst functional analysts: Greedy approximation with respect to bases in Banach spaces and nonlinear geometry of Banach spaces. This new material is intended to present these two directions of research for their intrinsic importance...
This text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too ...
The primary goal of this book is to present the theoretical foundation of the field of Euclidean Harmonic analysis. This book is Modern in that is contains more recent topics such as function spaces, atomic decompositions, singular integrals of nonconvolution type, and weighted inequalities. This book is mainly addressed to graduate students in mathematics. The prerequisites are satisfactory completion of courses in real and complex variables, and knowledge of classical Fourier analysis topics. This book is intended to present the selected topics in depth and stimulate further study....
The primary goal of this book is to present the theoretical foundation of the field of Euclidean Harmonic analysis. This book is Modern in that is ...
The primary goal of this book is to present the theoretical foundation of the field of Euclidean Harmonic analysis. This book contains the classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood-Paley theory. This book is mainly addressed to graduate students in mathematics. The prerequisites are satisfactory completion of courses in real and complex variables. This book is intended to present the selected topics in depth and stimulate further study.
This third edition includes a new chapter entitled...
The primary goal of this book is to present the theoretical foundation of the field of Euclidean Harmonic analysis. This book contains the classica...
This book is intended for a one-year graduate course on Lie groups and Lie algebras. The book goes beyond the representation theory of compact Lie groups, which is the basis of many texts, and provides a carefully chosen range of material to give the student the bigger picture. The book is organized to allow different paths through the material depending on one's interests. This second edition has substantial new material, including improved discussions of underlying principles, streamlining of some proofs, and many results and topics that were not in the first edition.
For compact...
This book is intended for a one-year graduate course on Lie groups and Lie algebras. The book goes beyond the representation theory of compact Lie ...
This text provides a masterful and systematic treatment of all the basic analytic and geometric aspects of Bergman's classic theory of the kernel and its invariance properties. These include calculation, invariance properties, boundary asymptotics, and asymptotic expansion of the Bergman kernel and metric. Moreover, it presents a unique compendium of results with applications to function theory, geometry, partial differential equations, and interpretations in the language of functional analysis, with emphasis on the several complex variables context. Several of these topics appear here for...
This text provides a masterful and systematic treatment of all the basic analytic and geometric aspects of Bergman's classic theory of the kernel and ...
This graduate text, while focusing on locally convex topological vector spaces, covers most of the general theory needed for application to other areas of functional analysis. Includes over 100 exercises with varying levels of difficulty.
This graduate text, while focusing on locally convex topological vector spaces, covers most of the general theory needed for application to other area...
This book provides a rigorous but elementary introduction to the theory of Markov Processes on a countable state space. Topics covered include: Doeblin's theory, general ergodic properties, and continuous time processes.
This book provides a rigorous but elementary introduction to the theory of Markov Processes on a countable state space. Topics covered include: Doebli...
