Uniform Distribution of Sequences (Dover Books on Mathematics) by L. Kuipers (PDF)

Description

The theory of uniform distribution began with Hermann Weyl’s celebrated paper of 1916. In later decades, the theory moved beyond its roots in diophantine approximations to provide common ground for topics as diverse as number theory, probability theory, functional analysis, and topological algebra. This book summarizes the theory’s development from its beginnings to the mid-1970s, with comprehensive coverage of both methods and their underlying principles.A practical introduction for students of number theory and analysis as well as a reference for researchers in the field, this book covers uniform distribution in compact spaces and in topological groups, in addition to examinations of sequences of integers and polynomials. Notes at the end of each section contain pertinent bibliographical references and a brief survey of additional results. Exercises range from simple applications of theorems to proofs of propositions that expand upon results stated in the text.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Clear, complete, and, unfortunately, not very well known. As the other reviewer notes, you can’t beat the price either. Every home (well, a home with a number theorist or a harmonic analyst) should have one.

⭐If we have a continuous function on the interval [0,1], then we can ask how to approximate its integral over this interval by a sum of the function evaluated at certain points in the interval. If the function changes a lot we will have to evaluate the function at points that are highly spread out (and numerous), to be able to see all these changes.Asking whether a sequence of real numbers is uniformly distributed is equivalent to asking whether a sequence of measures, each measure the normalized sum of delta measures placed at these real numbers, converges weak *-ly to the Lebesgue measure. Discrepancy aims at quantifying how quickly a sequence of measures converges to the Lebesgue measure.The first chapter of this book is on uniform distribution mod 1, and the second chapter is on discrepancy theory. I have only used these chapters; the other chapters are on uniform distribution in more general spaces than the unit interval. I wanted to learn about uniform distribution for a problem I was working on. I needed Koksma’s inequality and some facts about the discrepancy of the sequence nx, where x is an irrational number. I think that anyone doing analysis should spend at least a few hours with this book. There are good notes at the end of each section.

⭐The book is very deep on the subject.Is one of the most complet work about distribution mod 1.The book is well organized and leed the reader from the basis to specialistics arguments.Last but not least the price is very good.

⭐Not found.

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