arXiv subjects
Publications and source records attributed to Garth Warner.
The purpose of this book is two fold. (1) To give a systematic account of classical "zero theory" as developed by Jensen, Pólya, Titchmarsh, Cartwright, Levinson and others. (2) To set forth developments of a more recent nature with a view toward their possible application to the Riemann Hypothesis.
The purpose of this book is to lay out certain aspects of descriptive set theory. After initially establishing notation and generalities we proceed to the following topics: partitions, semirings, rings, $σ$-rings, $δ$-rings, products and sums, extension and generation. Extensive references and historical comments are included at the end of each section, as are further examples in the form of exercises and problems.
Here one will find a rigorous treatment of the simplest situation in Surface Area Theory, viz. the nonparametric case with domain the unit square in the plane. This is installment IV of a four part discussion of certain aspects of Real Analysis: Functions of a Single Variable, Curves and Length, Functions of Several Variables, and Surfaces and Area.
Apart from an account of classical preliminaries, this volume contains a systematic introduction to Sobolev spaces and functions of bounded variation with selected applications. This is installment III of a four part discussion of certain aspects of Real Analysis: Functions of a Single Variable, Curves and Length, Functions of Several Variables, and Surfaces and Area.
This is a systematic accounting of the classical theorems of Jordan and Tonelli, as well as an introduction to the theory of the Weierstrass integral which in its definitive form is due to Cesari. This is installment II of a four part discussion of certain aspects of Real Analysis: Functions of a Single Variable, Curves and Length, Functions of Several Variables, and Surfaces and Area.
These notes are a chapter in Real Analysis. While primarily standard, the reader will find a discussion of certain topics that are ordinarily not covered in the usual accounts. For example, the notion of bounded variation in the sense of Cesari is introduced. This is Volume 1 of 4, to be followed by Curves and Length, Functions of Several Variables, and Surfaces and Area.
The purpose of this book is to provide an introduction to one of the fundamental tools of abstract harmonic analysis, namely the Selberg trace formula.
This book is an account of certain topics in general and algebraic topology. Instead of laying out a synopsis of each chapter, here is a sample of some of what is taken up: 1) Nilpotency and its role in homotopy theory. 2) Bousfield's theory of the localization of spaces and spectra. 3) Homotopy limits and colimits and their applications. 4) The James construction, symmetric products, and the Dold$-$Thom theorem. 5) Brown and Adams representability in the setting of triangulated categories 6) Operads and the May$-$Thomason theorem on the uniqueness of infinite loop space machines. 7) The plus construction and theorems A and B of Quillen. 8) Hopkins' global picture of stable homotopy theory. 9) Model categories, cofibration categories, and Waldhausen categories. 10) The Dugundji extension theorem and its consequences.
The purpose of this book is to provide an introduction to period theory and then to place it within the matrix of recursive function theory.
In this book there will be found an introduction to transcendental number theory, starting at the beginning and ending at the frontiers. The emphasis is on the conceptual aspects of the subject, thus the effective theory has been more or less completely ignored, as has been the theory of $E$-functions and $G$-functions. Still, a fair amount of ground is covered and while I take certain results without proof, this is done primarily so as not to get bogged down in technicalities, otherwise the exposition is detailed and little is left to the reader.
This exposition begins with a systematic account of the theory of group schemes, ultimately specializing to algebraic tori.
The objective of this article is to give an introduction to p-adic analysis along the lines of Tate's thesis, as well as incorporating material of a more recent vintage, for example Weil groups.
This paper initiates a study into the contribution to the trace provided by the conjugacy classes.
The purpose of this note is to announce the results of our investigation into the role played by the continuous spectrum in the development of the Selberg trace formula vis-à-vis a pair $(G,Γ)$. For the sake of simplicity, we shall restrict ourselves to a "rank-2" situation, a case in point being when $G = \textbf{SL}(3,\mathbb{R}), \ Γ= \textbf{SL}(3,\mathbb{Z})$. Full details (in all generality) will appear elsewhere.