Author : Peter Gustav Lejeune Dirichlet
Publisher : American Mathematical Soc.
Page : 297 pages
File Size : 29,55 MB
Release : 1999
Category : Mathematics
ISBN : 0821820176
Lectures on Number Theory is the first of its kind on the subject matter. It covers most of the topics that are standard in a modern first course on number theory, but also includes Dirichlet's famous results on class numbers and primes in arithmetic progressions.
Author : Kai Wang Ng
Publisher : John Wiley & Sons
Page : 259 pages
File Size : 27,15 MB
Release : 2011-05-03
Category : Mathematics
ISBN : 1119998417
The Dirichlet distribution appears in many areas of application, which include modelling of compositional data, Bayesian analysis, statistical genetics, and nonparametric inference. This book provides a comprehensive review of the Dirichlet distribution and two extended versions, the Grouped Dirichlet Distribution (GDD) and the Nested Dirichlet Distribution (NDD), arising from likelihood and Bayesian analysis of incomplete categorical data and survey data with non-response. The theoretical properties and applications are also reviewed in detail for other related distributions, such as the inverted Dirichlet distribution, Dirichlet-multinomial distribution, the truncated Dirichlet distribution, the generalized Dirichlet distribution, Hyper-Dirichlet distribution, scaled Dirichlet distribution, mixed Dirichlet distribution, Liouville distribution, and the generalized Liouville distribution. Key Features: Presents many of the results and applications that are scattered throughout the literature in one single volume. Looks at the most recent results such as survival function and characteristic function for the uniform distributions over the hyper-plane and simplex; distribution for linear function of Dirichlet components; estimation via the expectation-maximization gradient algorithm and application; etc. Likelihood and Bayesian analyses of incomplete categorical data by using GDD, NDD, and the generalized Dirichlet distribution are illustrated in detail through the EM algorithm and data augmentation structure. Presents a systematic exposition of the Dirichlet-multinomial distribution for multinomial data with extra variation which cannot be handled by the multinomial distribution. S-plus/R codes are featured along with practical examples illustrating the methods. Practitioners and researchers working in areas such as medical science, biological science and social science will benefit from this book.
Author : Zhi-Ming Ma
Publisher : Springer Science & Business Media
Page : 215 pages
File Size : 39,89 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3642777392
The purpose of this book is to give a streamlined introduction to the theory of (not necessarily symmetric) Dirichlet forms on general state spaces. It includes both the analytic and the probabilistic part of the theory up to and including the construction of an associated Markov process. It is based on recent joint work of S. Albeverio and the two authors and on a one-year-course on Dirichlet forms taught by the second named author at the University of Bonn in 1990/9l. It addresses both researchers and graduate students who require a quick but complete introduction to the theory. Prerequisites are a basic course in probabil ity theory (including elementary martingale theory up to the optional sampling theorem) and a sound knowledge of measure theory (as, for example, to be found in Part I of H. Bauer [B 78]). Furthermore, an elementary course on lin ear operators on Banach and Hilbert spaces (but without spectral theory) and a course on Markov processes would be helpful though most of the material needed is included here.
Author : Godfrey Harold Hardy
Publisher :
Page : 100 pages
File Size : 35,28 MB
Release : 1915
Category : Mathematics
ISBN :
This classic work by two distinguished mathematicians explains theory and formulas behind Dirichlet's series and offers first systematic account of Riesz's theory of summation of series by typical means. 1915 edition.
Author : Nicola Arcozzi
Publisher : American Mathematical Soc.
Page : 559 pages
File Size : 32,4 MB
Release : 2019-09-03
Category : Mathematics
ISBN : 1470450828
The study of the classical Dirichlet space is one of the central topics on the intersection of the theory of holomorphic functions and functional analysis. It was introduced about100 years ago and continues to be an area of active current research. The theory is related to such important themes as multipliers, reproducing kernels, and Besov spaces, among others. The authors present the theory of the Dirichlet space and related spaces starting with classical results and including some quite recent achievements like Dirichlet-type spaces of functions in several complex variables and the corona problem. The first part of this book is an introduction to the function theory and operator theory of the classical Dirichlet space, a space of holomorphic functions on the unit disk defined by a smoothness criterion. The Dirichlet space is also a Hilbert space with a reproducing kernel, and is the model for the dyadic Dirichlet space, a sequence space defined on the dyadic tree. These various viewpoints are used to study a range of topics including the Pick property, multipliers, Carleson measures, boundary values, zero sets, interpolating sequences, the local Dirichlet integral, shift invariant subspaces, and Hankel forms. Recurring themes include analogies, sometimes weak and sometimes strong, with the classical Hardy space; and the analogy with the dyadic Dirichlet space. The final chapters of the book focus on Besov spaces of holomorphic functions on the complex unit ball, a class of Banach spaces generalizing the Dirichlet space. Additional techniques are developed to work with the nonisotropic complex geometry, including a useful invariant definition of local oscillation and a sophisticated variation on the dyadic Dirichlet space. Descriptions are obtained of multipliers, Carleson measures, interpolating sequences, and multiplier interpolating sequences; estimates are obtained to prove corona theorems.
Author : Richard Courant
Publisher : Courier Corporation
Page : 354 pages
File Size : 35,25 MB
Release : 2005-01-01
Category : Mathematics
ISBN : 0486445526
Originally published: New York: Interscience Publishers, 1950, in series: Pure and applied mathematics (Interscience Publishers); v. 3.
Author : Goro Shimura
Publisher : Springer Science & Business Media
Page : 151 pages
File Size : 46,51 MB
Release : 2007-08-06
Category : Mathematics
ISBN : 0387724745
A book on any mathematical subject beyond the textbook level is of little value unless it contains new ideas and new perspectives. It helps to include new results, provided that they give the reader new insights and are presented along with known old results in a clear exposition. It is with this philosophy that the author writes this volume. The two subjects, Dirichlet series and modular forms, are traditional subjects, but here they are treated in both orthodox and unorthodox ways. Regardless of the unorthodox treatment, the author has made the book accessible to those who are not familiar with such topics by including plenty of expository material.
Author : R. Courant
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 12,1 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461299179
It has always been a temptation for mathematicians to present the crystallized product of their thoughts as a deductive general theory and to relegate the individual mathematical phenomenon into the role of an example. The reader who submits to the dogmatic form will be easily indoctrinated. Enlightenment, however, must come from an understanding of motives; live mathematical development springs from specific natural problems which can be easily understood, but whose solutions are difficult and demand new methods of more general significance. The present book deals with subjects of this category. It is written in a style which, as the author hopes, expresses adequately the balance and tension between the individuality of mathematical objects and the generality of mathematical methods. The author has been interested in Dirichlet's Principle and its various applications since his days as a student under David Hilbert. Plans for writing a book on these topics were revived when Jesse Douglas' work suggested to him a close connection between Dirichlet's Principle and basic problems concerning minimal sur faces. But war work and other duties intervened; even now, after much delay, the book appears in a much less polished and complete form than the author would have liked."
Author : Christian G. Simader
Publisher : Springer
Page : 243 pages
File Size : 11,28 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540375899
Author : Vladimir Scheffer
Publisher : World Scientific
Page : 973 pages
File Size : 22,35 MB
Release : 2000-06-30
Category : Mathematics
ISBN : 9814494119
Fred Almgren exploited the excess method for proving regularity theorems in the calculus of variations. His techniques yielded Hölder continuous differentiability except for a small closed singular set. In the sixties and seventies Almgren refined and generalized his methods. Between 1974 and 1984 he wrote a 1,700-page proof that was his most ambitious development of his ground-breaking ideas. Originally, this monograph was available only as a three-volume work of limited circulation. The entire text is faithfully reproduced here.This book gives a complete proof of the interior regularity of an area-minimizing rectifiable current up to Hausdorff codimension 2. The argument uses the theory of Q-valued functions, which is developed in detail. For example, this work shows how first variation estimates from squash and squeeze deformations yield a monotonicity theorem for the normalized frequency of oscillation of a Q-valued function that minimizes a generalized Dirichlet integral. The principal features of the book include an extension theorem analogous to Kirszbraun's theorem and theorems on the approximation in mass of nearly flat mass-minimizing rectifiable currents by graphs and images of Lipschitz Q-valued functions.
