This book is written to be a convenient reference for the working scientist, student, or engineer who needs to know and use basic concepts in complex analysis. It is not a book of mathematical theory. It is instead a book of mathematical practice. All the basic ideas of complex analysis, as well as many typical applica- tions, are treated. Since we are not developing theory and proofs, we have not been obliged to conform to a strict logical ordering of topics. Instead, topics have been organized for ease of reference, so that cognate topics appear in one place. Required background for reading...
This book is written to be a convenient reference for the working scientist, student, or engineer who needs to know and use basic concepts in complex ...
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 ...
Foundations of Analysis covers the basics of real analysis for a one- or two-semester course. In a straightforward and concise way, it helps students understand the key ideas and apply the theorems. The book s accessible approach will appeal to a wide range of students and instructors.
Each section begins with a boxed introduction that familiarizes students with the upcoming topics and sets the stage for the work to be done. Each section ends with several questions that ask students to review what they have just learned. The text is also scattered with notes...
Foundations of Analysis covers the basics of real analysis for a one- or two-semester course. In a straightforward and concise way...
This concise, well-written handbook provides a distillation of real variable theory with a particular focus on the subject's significant applications to differential equations and Fourier analysis. Ample examples and brief explanations---with very few proofs and little axiomatic machinery---are used to highlight all the major results of real analysis, from the basics of sequences and series to the more advanced concepts of Taylor and Fourier series, Baire Category, and the Weierstrass Approximation Theorem. Replete with realistic, meaningful applications to differential equations, boundary...
This concise, well-written handbook provides a distillation of real variable theory with a particular focus on the subject's significant applicatio...
Key topics in the theory of real analytic functions are covered in this text, and are rather difficult to pry out of the mathematics literature.; This expanded and updated 2nd ed. will be published out of Boston in Birkhauser Adavaned Texts series.; Many historical remarks, examples, references and an excellent index should encourage the reader study this valuable and exciting theory.; Superior advanced textbook or monograph for a graduate course or seminars on real analytic functions.; New to the second edition a revised and comprehensive treatment of the Faa de Bruno formula, topologies on...
Key topics in the theory of real analytic functions are covered in this text, and are rather difficult to pry out of the mathematics literature.; This...
Logic is, and should be, the core subject area of modern mathemat- ics. The blueprint for twentieth century mathematical thought, thanks to Hilbert and Bourbaki, is the axiomatic development of the subject. As a result, logic plays a central conceptual role. At the same time, mathematical logic has grown into one of the most recondite areas of mathematics. Most of modern logic is inaccessible to all but the special- ist. Yet there is a need for many mathematical scientists-not just those engaged in mathematical research-to become conversant with the key ideas of logic. The Handbook of...
Logic is, and should be, the core subject area of modern mathemat- ics. The blueprint for twentieth century mathematical thought, thanks to Hilbert an...
The analysis of Euclidean space is well-developed. The classical Lie groups that act naturally on Euclidean space-the rotations, dilations, and trans- lations-have both shaped and guided this development. In particular, the Fourier transform and the theory of translation invariant operators (convolution transforms) have played a central role in this analysis. Much modern work in analysis takes place on a domain in space. In this context the tools, perforce, must be different. No longer can we expect there to be symmetries. Correspondingly, there is no longer any natural way to apply the...
The analysis of Euclidean space is well-developed. The classical Lie groups that act naturally on Euclidean space-the rotations, dilations, and trans-...
Mathematics is a poem. It is a lucid, sensual, precise exposition of beautiful ideas directed to specific goals. It is worthwhile to have as broad a cross-section of mankind as possible be conversant with what goes on in mathematics. Just as everyone knows that the Internet is a powerful and important tool for communication, so everyone should know that the Poincare conjecture gives us important information about the shape of our universe. Just as every responsible citizen realizes that the mass-production automobile was pioneered by Henry Ford, so everyone should know that the P/NP...
Mathematics is a poem. It is a lucid, sensual, precise exposition of beautiful ideas directed to specific goals. It is worthwhile to have as broad ...
The purpose of the corona workshop was toconsider the corona problem in both one and several complex variables, both in the context of function theory and harmonic analysis as well as the context of operator theory and functional analysis. It was held in June 2012 at the Fields Institute in Toronto, and attended by about fifty mathematicians. This volume validates and commemorates the workshop, and records some of the ideas that were developed within.
The corona problem dates back to 1941. It has exerted a powerful influence over mathematical analysis for nearly 75 years. There is...
The purpose of the corona workshop was toconsider the corona problem in both one and several complex variables, both in the context of function the...
Convexity is an ancient idea going back to Archimedes. Used sporadically in the mathematical literature over the centuries, today it is a flourishing area of research and a mathematical subject in its own right. Convexity is used in optimization theory, functional analysis, complex analysis, and other parts of mathematics.
Convex Analysis introduces analytic tools for studying convexity and provides analytical applications of the concept. The book includes a general background on classical geometric theory which allows readers to obtain a glimpse of how modern...
Convexity is an ancient idea going back to Archimedes. Used sporadically in the mathematical literature over the centuries, today it is a f...
