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Logical Foundations of Mathematics and Computational Complexity
The two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. Logical Foundations of …
Hardy Operators, Function Spaces and Embeddings
Classical Sobolev spaces, based on Lebesgue spaces on an underlying domain with smooth boundary, are not only of considerable intrinsic interest but have for many years proved to …
General Galois Geometries
This book is the second edition of the third and last volume of a treatise on projective spaces over a finite field, also known as Galois geometries. This volume completes the …
Regular Functions of a Quaternionic Variable
This book surveys the foundations of the theory of slice regular functions over the quaternions, introduced in 2006, and gives an overview of its generalizations and …
Convex Polyhedra
Convex Polyhedra is one of the classics in geometry. There simply is no other book with so many of the aspects of the theory of 3-dimensional convex polyhedra in a comparable way, …
Hardy Spaces on the Euclidean Space
"Still waters run deep." This proverb expresses exactly how a mathematician Akihito Uchiyama and his works were. He was not celebrated except in the field of harmonic analysis, and …
Serre's Problem on Projective Modules
“Serre’s Conjecture”, for the most part of the second half of the 20th century, - ferred to the famous statement made by J. -P. Serre in 1955, to the effect that one did not know …
Discrete Energy on Rectifiable Sets
This book aims to provide an introduction to the broad and dynamic subject of discrete energy problems and point configurations. Written by leading authorities on the topic, this …
Brownian Motion, Obstacles and Random Media
The principal purpose of this book is to provide an account of the circle of ideas, results and techniques, which emerged roughly over the last ten years in the study of Brownian …
Functional Equations and Inequalities with Applications
Functional Equations and Inequalities with Applications presents a comprehensive, nearly encyclopedic, study of the classical topic of functional equations. Nowadays, the field of …
Dessins d'Enfants on Riemann Surfaces
This volume provides an introduction to dessins d'enfants and embeddings of bipartite graphs in compact Riemann surfaces. The first part of the book presents basic material, …
Dimension Theory of Hyperbolic Flows
The dimension theory of dynamical systems has progressively developed, especially over the last two decades, into an independent and extremely active field of research. Its main …