Kategoria BISAC: Mathematics >> Calculus

An understanding of the developments in classical analysis during the nineteenth century is vital to a full appreciation of the history of twentieth-century mathematical thought. It was during the nineteenth century that the diverse mathematical formulae of the eighteenth century were systematized and the properties of functions of real and complex variables clearly distinguished; and it was then that the calculus matured into the rigorous discipline of today, becoming in the process a dominant influence on mathematics and mathematical physics.

This Source Book, a sequel to D....

The interplay between analysis on Lie groups and the theory of special functions is well known. This monograph deals with the case of the Heisenberg group and the related expansions in terms of Hermite, special Hermite, and Laguerre functions. The main thrust of the book is to develop a concrete Littlewood-Paley-Stein theory for these expansions and use the theory to prove multiplier theorems. The questions of almost-everywhere and mean convergence of Bochner-Riesz means are also treated. Most of the results in this monograph appear for the first time in book form.

The first part of this monograph is devoted to a characterization of hypergeometric-like functions, that is, twists of hypergeometric functions in n-variables. These are treated as an (n+1) dimensional vector space of multivalued locally holomorphic functions defined on the space of n+3 tuples of distinct points on the projective line P modulo, the diagonal section of Auto P=m. For n=1, the characterization may be regarded as a generalization of Riemann's classical theorem characterizing hypergeometric functions by their exponents at...

This book contains an exposition of some of the main developments of the last twenty years in the following areas of harmonic analysis: singular integral and pseudo-differential operators, the theory of Hardy spaces, Lsup estimates involving oscillatory integrals and Fourier integral operators, relations of curvature to maximal inequalities, and connections with analysis on the Heisenberg group.

Written for advanced undergraduate and first-year graduate students, this book aims to introduce students to a serious level of p-adic analysis with important implications for number theory. The main object is the study of G-series, that is, power series y=aij=0 Ajxj with coefficients in an algebraic number field K. These series satisfy a linear differential equation Ly=0 with LIK(x) d/dx] and have non-zero radii of convergence for each imbedding of K into the complex numbers. They have the further property that the common denominators of the first s...

The fifteen articles composing this volume focus on recent developments in complex analysis. Written by well-known researchers in complex analysis and related fields, they cover a wide spectrum of research using the methods of partial differential equations as well as differential and algebraic geometry. The topics include invariants of manifolds, the complex Neumann problem, complex dynamics, Ricci flows, the Abel-Radon transforms, the action of the Ricci curvature operator, locally symmetric manifolds, the maximum principle, very ampleness criterion, integrability of elliptic systems,...

Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested in non-standard analysis. It treats in rich detail many...

Kurt Godel, mathematician and logician, was one of the most influential thinkers of the twentieth century. Godel fled Nazi Germany, fearing for his Jewish wife and fed up with Nazi interference in the affairs of the mathematics institute at the University of Gottingen. In 1933 he settled at the Institute for Advanced Study in Princeton, where he joined the group of world-famous mathematicians who made up its original faculty.

His 1940 book, better known by its short title, The Consistency of the Continuum Hypothesis, is a classic of modern mathematics. The continuum...

This book contains a valuable discussion of renormalization through the addition of counterterms to the Lagrangian, giving the first complete proof of the cancellation of all divergences in an arbitrary interaction. The author also introduces a new method of renormalizing an arbitrary Feynman amplitude, a method that is simpler than previous approaches and can be used to study the renormalized perturbation series in quantum field theory.

Intended for researchers in Riemann surfaces, this volume summarizes a significant portion of the work done in the field during the years 1966 to 1971.

A survey, thorough and timely, of the singularities of two-dimensional normal complex analytic varieties, the volume summarizes the results obtained since Hirzebruch's thesis (1953) and presents new contributions. First, the singularity is resolved and shown to be classified by its resolution; then, resolutions are classed by the use of spaces with nilpotents; finally, the spaces with nilpotents are determined by means of the local ring structure of the singularity.

The present monograph grew out of the fifth set of Hermann Weyl Lectures, given by Professor Griffiths at the Institute for Advanced Study, Princeton, in fall 1974.

In Chapter 1 the author discusses Emile Borel's proof and the classical Jensen theorem, order of growth of entire analytic sets, order functions for entire holomorphic mappings, classical indicators of orders of growth, and entire functions and varieties of finite order.

Chapter 2 is devoted to the appearance of curvature, and Chapter 3 considers the defect relations. The author considers the lemma on the...

Based on lectures in Erevan, this exposition of ergodic theory contains a rich collection of examples well chosen to introduce the reader to the main themes of the subject. Topics discussed include existence of invariant measures, geodesic flows on Riemannian manifolds, ergodic theory of an ideal gas, and entropy of dynamical systems.

The application by Fadeev and Pavlov of the Lax-Phillips scattering theory to the automorphic wave equation led Professors Lax and Phillips to reexamine this development within the framework of their theory. This volume sets forth the results of that work in the form of new or more straightforward treatments of the spectral theory of the Laplace-Beltrami operator over fundamental domains of finite area; the meromorphic character over the whole complex plane of the Eisenstein series; and the Selberg trace formula.

CONTENTS: 1. Introduction. 2. An abstract scattering theory. 3. A...

Based on a seminar sponsored by the Institute for Advanced Study in 1977-1978, this set of papers introduces micro-local analysis concisely and clearly to mathematicians with an analytical background. The papers treat the theory of microfunctions and applications such as boundary values of elliptic partial differential equations, propagation of singularities in the vicinity of degenerate characteristics, holonomic systems, Feynman integrals from the hyperfunction point of view, and harmonic analysis on Lie groups.