Epstein, Charles L.Overview
Publication Timeline
Most widely held works by
Charles L Epstein
Degenerate diffusion operators arising in population biology
by Charles L Epstein
(
)
8 editions published in 2013 in English and held by 877 WorldCat member libraries worldwide This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the Martingale problem and therefore the existence of the associated Markov process. Charles Epstein and Rafe Mazzeo use an ""integral kernel method"" to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic proces
Introduction to the mathematics of medical imaging
by Charles L Epstein
(
Book
)
22 editions published between 2003 and 2008 in English and held by 373 WorldCat member libraries worldwide At the heart of every medical imaging technology is a sophisticated mathematical model of the measurement process and an algorithm to reconstruct an image from the measured data. This book provides a firm foundation in the mathematical tools used to model the measurements and derive the reconstruction algorithms used in most of these modalities. The text uses Xray computed tomography (Xray CT) as a 'pedagogical machine' to illustrate important ideas and its extensive discussion of background material makes the more advanced mathematical topics accessible to people with a less formal mathematical education. This new edition contains a chapter on magnetic resonance imaging (MRI), a revised section on the relationship between the continuum and discrete Fourier transforms, an improved description of the gridding method, and new sections on both Grangreat's formula and noise analysis in MRimaging. Mathematical concepts are illuminated with over 200 illustrations and numerous exercises
The spectral theory of geometrically periodic hyperbolic 3manifolds
by Charles L Epstein
(
Book
)
13 editions published between 1983 and 1985 in English and held by 234 WorldCat member libraries worldwide
Advanced real analysis along with a companion volume, Basic real analysis
by Anthony W Knapp
(
)
3 editions published in 2005 in English and held by 20 WorldCat member libraries worldwide Advanced€Real Analysis systematically develops the concepts and tools that are vital to every mathematician, whether pure or applied, aspiring or established. This work presents a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics. Key topics and features: . Early chapters treat the fundamentals of real variables, the theory of Fourier series for the Riemann integral, and the theoretical underpinnings of multivariable calculus and differential equations . Subsequent chapters develop measure theory, pointset topology, Fourier series for the Lebesgue integral, and the basics of Banach and Hilbert spaces . Later chapters provide a higherlevel view of the interaction between real analysis and algebra, including functional analysis, partial differential equations, and further topics in Fourier analysis . Throughout the text are problems that develop and illuminate aspects of the theory of probability . Includes many examples and hundreds of problems, and a chapter gives hints or complete solutions for most of the problems It requires of the reader only familiarity with some linear algebra and real variable theory, a few weeks' worth of group theory, and an acquaintance with proofs. Because it focuses on what every young mathematician needs to know about real analysis, this book is ideal both as a course text and for selfstudy, especially for graduate students preparing for qualifying examinations. Its scope and unique approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, math physics, and applied differential equations. Indeed, the clarity and breadth of Advanced Real Analysis make it a welcome addition to the personal library of every mathematician. TOC:Preface * Theory of calculus in one real variable * Metric spaces * Theory of differential calculus in several variables * Theory of ordinary differential equations and systems * Riemann integration in several variables * Abstract measure theory and Lebesgue measure * Measure theory for Euclidean space * Fourier transform in R^N * L^p spaces * Further topics in abstract measure theory * Topological spaces * Integration on locally compact spaces * Haar measure * Hilbert and Banach spaces * Distributions and their application to PDEs * References * Index
Cornerstones
(
)
in English and held by 4 WorldCat member libraries worldwide
A stable manifold theorem for the curve shortening equation
by Charles L Epstein
(
Book
)
1 edition published in 1986 in English and held by 2 WorldCat member libraries worldwide
A relative index on the space of embeddable CRstructures
by Charles L Epstein
(
Book
)
2 editions published in 1995 in English and held by 2 WorldCat member libraries worldwide
Mathematics of medical imaging
by Charles L Epstein
(
Book
)
1 edition published in 2003 in English and held by 1 WorldCat member library worldwide
Die Bedeutung der SchuÌˆlerbibliotheken : mit einem Anhang: Verzeichnis empfehlenswerter Jugendschriften
by Charles L Epstein
(
Book
)
1 edition published in 1901 in German and held by 1 WorldCat member library worldwide Audience Level
Related Identities
Associated Subjects
Diagnostic imagingMathematics Differential equations, Partial Distribution (Probability theory) Elliptic operators Fourier analysis Functional analysis Global analysis (Mathematics) Markov processes Mathematical analysis Mathematics Medical physicsMathematics Population biologyMathematical models Spectral theory (Mathematics) Threemanifolds (Topology)

Alternative Names
Epstein, C. 1957
Epstein, C. L. 1957
Epstein, Charles 1957
Languages
Covers
