Multi Parameter Hardy Spaces Theory And Endpoint Estimates For Multi Parameter Singular Integrals

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Multi-Parameter Hardy Spaces Theory and Endpoint Estimates for Multi-Parameter Singular Integrals

Author: Guozhen Lu
language: en
Publisher: American Mathematical Society
Release Date: 2023-01-18
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Finite Fields, with Applications to Combinatorics

Author: Kannan Soundararajan
language: en
Publisher: American Mathematical Society
Release Date: 2022-11-09
This book uses finite field theory as a hook to introduce the reader to a range of ideas from algebra and number theory. It constructs all finite fields from scratch and shows that they are unique up to isomorphism. As a payoff, several combinatorial applications of finite fields are given: Sidon sets and perfect difference sets, de Bruijn sequences and a magic trick of Persi Diaconis, and the polynomial time algorithm for primality testing due to Agrawal, Kayal and Saxena. The book forms the basis for a one term intensive course with students meeting weekly for multiple lectures and a discussion session. Readers can expect to develop familiarity with ideas in algebra (groups, rings and fields), and elementary number theory, which would help with later classes where these are developed in greater detail. And they will enjoy seeing the AKS primality test application tying together the many disparate topics from the book. The pre-requisites for reading this book are minimal: familiarity with proof writing, some linear algebra, and one variable calculus is assumed. This book is aimed at incoming undergraduate students with a strong interest in mathematics or computer science.
Maximal Subellipticity

Author: Brian Street
language: en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date: 2023-07-04
Maximally subelliptic partial differential equations (PDEs) are a far-reaching generalization of elliptic PDEs. Elliptic PDEs hold a special place: sharp results are known for general linear and even fully nonlinear elliptic PDEs. Over the past half-century, important results for elliptic PDEs have been generalized to maximally subelliptic PDEs. This text presents this theory and generalizes the sharp, interior regularity theory for general linear and fully nonlinear elliptic PDEs to the maximally subelliptic setting.