Author: Walter Rudin
Publisher: American Mathematical Soc.
ISBN: 9780821889084
Category : Mathematics
Languages : en
Pages : 100

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Author: Kehe Zhu
Publisher: Springer Science & Business Media
ISBN: 0387275398
Category : Mathematics
Languages : en
Pages : 281

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Can be used as a graduate text Contains many exercises Contains new results

Author: Manfred Stoll
Publisher: Cambridge University Press
ISBN: 0521468302
Category : Mathematics
Languages : en
Pages : 187

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Book Description
This monograph provides an introduction and a survey of recent results in potential theory with respect to the Laplace-Beltrami operator D in several complex variables, with special emphasis on the unit ball in Cn. Topics covered include Poisson-Szegö integrals on the ball, the Green's function for D and the Riesz decomposition theorem for invariant subharmonic functions. The extension to the ball of the classical Fatou theorem on non-tangible limits of Poisson integrals, and Littlewood's theorem on the existence of radial limits of subharmonic functions are covered in detail. The monograph also contains recent results on admissible and tangential boundary limits of Green potentials, and Lp inequalities for the invariant gradient of Green potentials. Applications of some of the results to Hp spaces, and weighted Bergman and Dirichlet spaces of invariant harmonic functions are included. The notes are self-contained, and should be accessible to anyone with some basic knowledge of several complex variables.

Author: Steven George Krantz
Publisher: American Mathematical Soc.
ISBN: 082180734X
Category : Mathematics
Languages : en
Pages : 216

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Book Description
This book brings into focus the synergistic interaction between analysis and geometry by examining a variety of topics in function theory, real analysis, harmonic analysis, several complex variables, and group actions. Krantz's approach is motivated by examples, both classical and modern, which highlight the symbiotic relationship between analysis and geometry. Creating a synthesis among a host of different topics, this book is useful to researchers in geometry and analysis and may be of interest to physicists, astronomers, and engineers in certain areas. The book is based on lectures presented at an NSF-CBMS Regional Conference held in May 1992.

Author: Hugh L. Montgomery
Publisher: American Mathematical Soc.
ISBN: 0821807374
Category : Mathematics
Languages : en
Pages : 242

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Book Description
This volume contains lectures presented by Hugh L. Montgomery at the NSF-CBMS Regional Conference held at Kansas State University in May 1990. The book focuses on important topics in analytic number theory that involve ideas from harmonic analysis. One particularly valuable aspect of the book is that it collects material that was either unpublished or that had appeared only in the research literature. The book should be a useful resource for harmonic analysts interested in moving into research in analytic number theory. In addition, it is suitable as a textbook in an advanced graduate topics course in number theory.

Author:
Publisher: American Mathematical Soc.
ISBN: 0821826395
Category :
Languages : en
Pages : 135

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Author: Jonathan R_osenberg
Publisher: American Mathematical Soc.
ISBN: 0821849220
Category : Mathematics
Languages : en
Pages : 122

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Book Description
String theory is the leading candidate for a physical theory that combines all the fundamental forces of nature, as well as the principles of relativity and quantum mechanics, into a mathematically elegant whole. The mathematical tools used by string theorists are highly sophisticated, and cover many areas of mathematics. As with the birth of quantum theory in the early 20th century, the mathematics has benefited at least as much as the physics from the collaboration. In this book, based on CBMS lectures given at Texas Christian University, Rosenberg describes some of the most recent interplay between string dualities and topology and operator algebras. The book is an interdisciplinary approach to duality symmetries in string theory. It can be read by either mathematicians or theoretical physicists, and involves a more-or-less equal mixture of algebraic topology, operator algebras, and physics. There is also a bit of algebraic geometry, especially in the last chapter. The reader is assumed to be somewhat familiar with at least one of these four subjects, but not necessarily with all or even most of them. The main objective of the book is to show how several seemingly disparate subjects are closely linked with one another, and to give readers an overview of some areas of current research, even if this means that not everything is covered systematically.

Author: Zhenghan Wang
Publisher: American Mathematical Soc.
ISBN: 0821849301
Category : Computers
Languages : en
Pages : 134

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Book Description
Topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories. In this approach, information is stored in the lowest energy states of many-anyon systems and processed by braiding non-abelian anyons. The computational answer is accessed by bringing anyons together and observing the result. Besides its theoretical esthetic appeal, the practical merit of the topological approach lies in its error-minimizing hypothetical hardware: topological phases of matter are fault-avoiding or deaf to most local noises, and unitary gates are implemented with exponential accuracy. Experimental realizations are pursued in systems such as fractional quantum Hall liquids and topological insulators. This book expands on the author's CBMS lectures on knots and topological quantum computing and is intended as a primer for mathematically inclined graduate students. With an emphasis on introducing basic notions and current research, this book gives the first coherent account of the field, covering a wide range of topics: Temperley-Lieb-Jones theory, the quantum circuit model, ribbon fusion category theory, topological quantum field theory, anyon theory, additive approximation of the Jones polynomial, anyonic quantum computing models, and mathematical models of topological phases of matter.

Author: Walter Rudin
Publisher: American Mathematical Soc.
ISBN: 0821807137
Category : Mathematics
Languages : en
Pages : 96

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Book Description
Uses as a starting point A B Aleksandrov's proof that nonconstant inner functions exist in the unit ball $B$ of $C DEGREESn$. This title simplifies the construction of such functions by using certain homogeneous polynomials discovered by Ryll and Wojtaszczyk; this yields solutions to a large number of pr

Author: Craig Huneke
Publisher: American Mathematical Soc.
ISBN: 082180412X
Category : Mathematics
Languages : en
Pages : 152

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Book Description
This monograph deals with the theory of tight closure and its applications. The contents are based on ten talks given at a CBMS conference held at North Dakota State University in June 1995.