Part of Cambridge Studies in Advanced Mathematics
Publication planned for: April 2019
availability: Not yet published - available from April 2019
format: Hardback
isbn: 9781107184541
The theory of Hardy spaces is a cornerstone of modern analysis. It combines
techniques from functional analysis, the theory of analytic functions and
Lesbesgue integration to create a powerful tool for many applications,
pure and applied, from signal processing and Fourier analysis to maximum
modulus principles and the Riemann zeta function. This book, aimed at beginning
graduate students, introduces and develops the classical results on Hardy
spaces and applies them to fundamental concrete problems in analysis. The
results are illustrated with numerous solved exercises that also introduce
subsidiary topics and recent developments. The reader's understanding of
the current state of the field, as well as its history, are further aided
by engaging accounts of important contributors and by the surveys of recent
advances (with commented reference lists) that end each chapter. Such broad
coverage makes this book the ideal source on Hardy spaces.
A complete introduction to Hardy spaces, including classical results and applications, accounts of the field's history, and surveys of recent developments
Numerous exercises and solutions illustrate the theory and introduce further applications
Suitable for beginning graduate students; it includes a concise account of the necessary background from analysis
The origins of the subject
1. The space H2(T) an archetype of an invariant subspace
2. Classes Hp(D). Canonical factorisation. First applications
3. The V. I. Smirnov class D and the maximum principle
4. An introduction to weighted Fourier analysis
5. Harmonic analysis in the service of stationary filtering
6. The Riemann hypothesis, dilations, and H2 in the Hilbert multi-disk
Appendix A. Key notions of integration
Appendix B. Key notions of complex analysis
Appendix C. Key notions of Hilbert spaces
Appendix D. Key notions of Banach spaces
Appendix E. Key notions of linear operators
References
Notation
Index.
Hardback
February 1, 2019 Forthcoming
Textbook - 512 Pages - 20 B/W Illustrations
ISBN 9781138580886 - CAT# K376221
Variational Techniques for Elliptic Partial Differential Equations, intended
for graduate students studying applied math, analysis, and/or numerical
analysis, provides the necessary tools to understand the structure and
solvability of elliptic partial differential equations. Beginning with
the necessary definitions and theorems from distribution theory, the book
gradually builds the functional analytic framework for studying elliptic
PDE using variational formulations. Rather than introducing all of the
prerequisites in the first chapters, it is the introduction of new problems
which motivates the development of the associated
analytical tools. In this way the student who is encountering this material
for the first time will be aware of exactly what theory is needed, and
for which problems.
I Fundamentals
1 Distributions
2 The homogeneous Dirichlet problem
3 Lipschitz transformations and Lipschitz domains
4 The nonhomogeneous Dirichlet problem
5 Nonsymmetric and complex problems
6 Neumann boundary conditions
7 Poincare inequalities and Neumann problems
8 Compact perturbations of coercive problems
9 Eigenvalues of elliptic operators
II Extensions and Applications
10 Mixed problems
11 Advanced mixed problems
12 Nonlinear problems
13 Fourier representation of Sobolev spaces
14 Layer potentials
15 A collection of elliptic problems
16 Curl spaces and Maxwell's equations
17 Elliptic equations on boundaries
A Review material
B Glossary
CBMS Regional Conference Series in Mathematics Volume: 128
2018; 266 pp; Softcover
MSC: Primary 28; 81; 11; 60; 42; 37;
Print ISBN: 978-1-4704-4880-6
There is a recent and increasing interest in harmonic analysis of non-smooth
geometries. Real-world examples where these types of geometry appear include
large computer networks, relationships in datasets, and fractal structures
such as those found in crystalline substances, light scattering, and other
natural phenomena where dynamical systems are present.
Notions of harmonic analysis focus on transforms and expansions and involve
dual variables. In this book on smooth and non-smooth harmonic analysis,
the notion of dual variables will be adapted to fractals. In addition to
harmonic analysis via Fourier duality, the author also covers multiresolution
wavelet approaches as well as a third tool, namely, L2 spaces derived from
appropriate Gaussian processes. The book is based on a series of ten lectures
delivered in June 2018 at a CBMS conference held at Iowa State University.
Undergraduate and graduate students and researchers interested in harmonic analysis and fractals.
2018 Paperback (ISBN 9781571463661)
To Be Published: 17 October 2018
Paperback
148 pages
This is the eleventh issue (Vol. 6, No. 1, July 2018) of the Notices of the International Congress of Chinese Mathematicians (or ICCM Notices, for short),
the official periodical of the ICCM organization.
Published semi-annually, the Notices bring news, research, and presentation
of various perspectives, relevant to Chinese mathematics development and
education.
Readers of the Notices will find research papers on various topics by prominent
experts from around the world, interesting and timely articles on current
applications and trends, biographical and historical essays, profiles of
important institutions of research and learning, and more.
Surveys in Differential Geometry Volume 22 (2017)
To Be Published: 31 October 2018
Hardcover
414 pages
In 1967, C.-C. Hsiung at Lehigh University had the vision to form the Journal
of Differential Geometry (JDG) a journal dedicated to geometry alone. On
the journalfs fiftieth anniversary in 2017, a distinguished group of geometers
gathered to present their papers at the annual JDG geometry and topology
conference at Harvard University.
This volume presents several of those papers, which include: Denis Auroux
on speculations on homological mirror symmetry for hypersurfaces in CnCn;
Frances Kirwan on variation of non-reductive geometric invariant theory;
Camillo De Lellis on the Onsager theorem; Simon Donaldsonfs remarks on
G2G2-manifolds with boundary; Daniel Freed on equivariant Chern?Weil forms
and determinant lines; Kenji Fukaya on construction of Kuranishi structures
on the moduli spaces of pseudo-holomorphic disks; Larry Guth on recent
progress in quantitative topology; Blain Lawson on Lagrangian potential
theory and a Lagrangian equation of Monge?Ampere type; Alena Pirutka on
intersections of three-quadrics in P7P7; Bong Lian on period integrals
and tautological systems; Yujiro Kawamata on birational geometry and derived
categories; Fernando C. Marques on the space of cycles, a Weyl law for
minimal hypersurfaces, and Morse index estimates; Duong Phong on new curvature
flows in complex geometry; and Steve Zelditch on local and global analysis
of nodal sets.
Fractals and Dynamics in Mathematics, Science, and the Arts: Theory and Applications: Volume 3
https://doi.org/10.1142/11126 | March 2019
Pages: 110
ISBN: 978-981-3275-16-4 (hardcover)
The book describes a recently discovered random fractal space-filling algorithm
beginning with tessellations and Sierpinski, illustrating the relationship
to statistical geometry and bringing together all that is known about it
to a wider audience of mathematicians and scientists.
The algorithm claims to be universal in scope, in that it can fill any
spatial region with smaller and smaller fill regions of any shape. The
filling is complete in the limit of an infinite number of fill regions.
This book presents a descriptive development of the subject using the traditional
shapes of geometry such as discs, squares, and triangles. It contains a
detailed mathematical treatment of all that is currently known about the
algorithm, as well as a chapter on software implementation of the algorithm.
The mathematician will find a wealth of interesting conjectures supported
by numerical computation. Physicists are offered a model looking for an
application. The patterns generated are often quite interesting as abstract
art.
Introduction; Space-Filling Patterns
Squares and Rectangles
Triangles and Diamonds
Discs and Circular Arcs
Mixed and Irregular Shapes
Mixed and Irregular Shapes
Examples
The Statistical Geometry Algorithm
The Area-Perimeter Algorithm
Statistical Geometry in One Dimension
Do It Yourself
Students, mathematicians, physicists, professionals, and the general public who are interested in the fractal art of statistical geometry.