https://doi.org/10.1515/9783110750355
This work is solely dedicated to the study of both the one variable as well as the multidimensional Lorentz spaces
covering the theory of Lebesgue type spaces invariant by rearrangement. The authors provide proofs in full
detail for most theorems.
The self-contained text is valuable for advanced students and researchers.
Dedicated to the study of Lorentz Spaces in one and several variables.
Deep study of Classical Lorentz Spaces and covering Multidimensional Lorentz Spaces as well.
Rene Erlin Castillo, Nationale U of Colombia, Colombia; Hector Camilo Chaparro,
Nueva Granada Military University, Colombia.
In the series De Gruyter Textbook
https://doi.org/10.1515/9783110751185
The second edition of this well-received textbook is devoted to Combinatorics and Graph Theory, which are cornerstones
of Discrete Mathematics. Every section begins with simple model problems. Following their detailed analysis, the reader i
s led through the derivation of definitions, concepts, and methods for solving typical problems. Theorems then are
formulated, proved, and illustrated by more problems of increasing difficulty.
For a one- or two-semester undergraduate or an entry-level graduate course
Suitable for self-study
Over 700 problems, many of them with answers or tips
New chapter on applied properties of boolean functions
Alexander Kheyfits, The City University of New York, USA.
Hardback
Published: 10 January 2022 (Estimated)
256 Pages | 191 black and white illustrations
246x189mm
ISBN: 9780198869030
The Savilian Professorships in Geometry and Astronomy at Oxford University were founded in 1619 by Sir Henry Savile,
Distinguished scholar and Warden of Merton College. The Geometry chair, in particular, is the earliest University-based
mathematics professorship in England, predating the first Cambridge equivalent by about sixty years.
To celebrate the 400th anniversary of the founding of the geometry chair, a meeting was held at the Bodleian Library
in Oxford, and the talks presented at this meeting have formed the basis for this fully edited and lavishly illustrated book,
which outlines the first 400 years of Oxford's Savilian Professors of Geometry.
Starting with Henry Briggs, the co-inventor of logarithms, this volume proceeds via such figures as John Wallis, a founder
member of the Royal Society, and Edmond Halley, via the 19th-century figures of Stephen Rigaud, Baden Powell,
Henry Smith, and James Joseph Sylvester, to the 20th century and the present day.
Oxford's Savilian Professors of Geometry: The First 400 Years assumes no mathematical background, and should
therefore appeal to the interested general reader with an interest in mathematics and the sciences. It should also
be of interest to anyone interested in the history of mathematics or of the development of Oxford and its namesake
university. To all of these audiences it offers portraits of mathematicians at work and an accessible exposition
of historical mathematics in the context of its times.
Foreword, Francis Kirwan, DBE, FRS
List of the Savilian Professors of Geometry
1:Sir Henry Savile and the Early Professors, William Poole
2:John Wallis, Phillip Beeley and Benjamin Wardhaugh
3:A Century of Astronomers: From Halley to Rigaud, Christopher Hollings and Allan Chapman
4:Baden Powell and Henry Smith, Keith Hannabuss
5:James Joseph Sylvester, Karen Hunger Parshall
6:G. H. Hardy and E. C. Titchmarsh, Robin Wilson
7:From Michael Atiyah to the 21st Century, Frances Kirwan
8:Interview with Nigel Hitchin, Mark McCartney
Further Reading, Notes, and References
Softcover
ISBN: 978-3-030-54535-2
This textbook explores a selection of topics in complex analysis. From core material in the mainstream of complex
analysis itself, to tools that are widely used in other areas of mathematics, this versatile compilation offers a selection
of many different paths. Readers interested in complex analysis will appreciate the unique combination of topics and
connections collected in this book.
Beginning with a review of the main tools of complex analysis, harmonic analysis, and functional analysis, the authors
go on to present multiple different, self-contained avenues to proceed. Chapters on linear fractional transformations,
harmonic functions, and elliptic functions offer pathways to hyperbolic geometry, automorphic functions, and an intuitive
introduction to the Schwarzian derivative. The gamma, beta, and zeta functions lead into L-functions, while a chapter
on entire functions opens pathways to the Riemann hypothesis and Nevanlinna theory. Cauchy transforms give rise
to Hilbert and Fourier transforms, with an emphasis on the connection to complex analysis. Valuable additional topics i
nclude Riemann surfaces, steepest descent, tauberian theorems, and the Wiener?Hopf method.
Showcasing an array of accessible excursions, Explorations in Complex Functions is an ideal companion for graduate
students and researchers in analysis and number theory. Instructors will appreciate the many options for constructing
a second course in complex analysis that builds on a first course prerequisite; exercises complement the results
throughout.
ISBN: 978-3-030-89191-6
This book is devoted to the structure of the absolute Galois groups of certain algebraic extensions of the field of rational
numbers. Its main result, a theorem proved by the authors and Florian Pop in 2012, describes the absolute Galois group
of distinguished semi-local algebraic (and other) extensions of the rational numbers as free products of the free profinite
group on countably many generators and local Galois groups. This is an instance of a positive answer to the generalized
inverse problem of Galois theory.
Adopting both an arithmetic and probabilistic approach, the book carefully sets out the preliminary material needed to
prove the main theorem and its supporting results. In addition, it includes a description of Melnikov's construction of
free products of profinite groups and, for the first time in book form, an account of a generalization of the theory of
free products of profinite groups and their subgroups.
The book will be of interest to researchers in field arithmetic, Galois theory and profinite groups.
Field arithmeticSemi-local fieldsAbsolute Galois groupsHaar measureFree profinite product of profinite groupStrong
projectivityEmbedding problem
ISBN: 978-3-030-89006-3
This is the first monograph dedicated solely to regularities of group actions
Provides a broad overview of the subject from classical beginnings to areas of active current research
Provides a self-contained, accessible treatment of many topics that have previously only appeared in journals
This book presents the theory of optimal and critical regularities of groups of diffeomorphisms, from the classical
work of Denjoy and Herman, up through recent advances. Beginning with an investigation of regularity phenomena
for single diffeomorphisms, the book goes on to describes a circle of ideas surrounding Filipkiewicz's Theorem,
which recovers the smooth structure of a manifold from its full diffeomorphism group. Topics covered include the
simplicity of homeomorphism groups, differentiability of continuous Lie group actions, smooth conjugation of
diffeomorphism groups, and the reconstruction of spaces from group actions. Various classical and modern tools
are developed for controlling the dynamics of general finitely generated group actions on one-dimensional manifolds,
subject to regularity bounds, including material on Thompson's group F, nilpotent groups, right-angled Artin groups,
chain groups, finitely generated groups with prescribed critical regularities, and applications to foliation theory and
the study of mapping class groups.
The book will be of interest to researchers in geometric group theory.