Series: Springer Series in Statistics
1st ed. 2017, XVII, 230 p. 84 illus., 50 illus. in color.
Hardcover
ISBN 978-1-4939-7188-6
* Offers an accessible text to those with little or no exposure to
differential equations as modeling objects
* Updates and builds on techniques from the popular Functional Data
Analysis (Ramsay and Silverman, 2005)
* Opens up new opportunities for dynamical systems and presents
additional applications for previously analyzed data
This text focuses on the use of smoothing methods for developing and estimating
differential equations following recent developments in functional data analysis and
building on techniques described in Ramsay and Silverman (2005) Functional Data
Analysis. The central concept of a dynamical system as a buffer that translates sudden
changes in input into smooth controlled output responses has led to applications
of previously analyzed data, opening up entirely new opportunities for dynamical
systems. The technical level has been kept low so that those with little or no exposure
to differential equations as modeling objects can be brought into this data analysis
landscape. There are already many texts on the mathematical properties of ordinary
differential equations, or dynamic models, and there is a large literature distributed
over many fields on models for real world processes consisting of differential equations.
However, a researcher interested in fitting such a model to data, or a statistician interested
in the properties of differential equations estimated from data will find rather less to work
with. This book fills that gap.
Jim Ramsay, PhD, is Professor Emeritus of Psychology and an Associate Member in the
Department of Mathematics and Statistics at McGill University. He received his PhD from
Princeton University in 1966 in quantitative psychology. He has been President of the
Psychometric Society and the Statistical Society of Canada. He received the Gold Medal
in 1998 for his contributions to psychometrics and functional data analysis and Honorary
Membership in 2012 from the Statistical Society of Canada.
Series: Probability Theory and Stochastic Modelling, Vol. 86
1st ed. 2017, VIII, 370 p.
Hardcover
ISBN 978-1-4939-7254-8
* Provides a systematic study from linear equations to fully nonlinear equations
* Includes up-to-date developments in the field
* A powerful and convenient tool for financial engineering and stochastic optimization
* Accessible to graduate students and junior researchers
This book provides a systematic and accessible approach to stochastic differential
equations, backward stochastic differential equations, and their connection with partial
differential equations, as well as the recent development of the fully nonlinear theory,
including nonlinear expectation, second order backward stochastic differential equations,
and path dependent partial differential equations. Their main applications and numerical
algorithms, as well as many exercises, are included.
The book focuses on ideas and clarity, with most results having been solved from scratch
and most theories being motivated from applications. It can be considered a starting point
for junior researchers in the field, and can serve as a textbook for a two-semester graduate
course in probability theory and stochastic analysis. It is also accessible for graduate
students majoring in financial engineering.
Series: Trends in Mathematics
1st ed. 2017, Approx. 400 p.
Hardcover
ISBN 978-3-319-63593-4
* Contains presentations from the special session on Integrability and Geometry
This book features a selection of articles based on the XXXV Bia*owie*a Workshop on
Geometric Methods in Physics, 2016. The series of Bia*owie*a workshops, attended by a
community of experts at the crossroads of mathematics and physics, is a major annual
event in the field. The works in this book, based on presentations given at the workshop,
are previously unpublished, at the cutting edge of current research, typically grounded in
geometry and analysis, and with applications to classical and quantum physics. In 2016
the special session "Integrability and Geometry" in particular attracted pioneers and
leading specialists in the field.
Traditionally, the Bia*owie*a Workshop is followed by a School on Geometry and Physics,
for advanced graduate students and early-career researchers, and the book also includes
extended abstracts of the lecture series.
Series: Springer Monographs in Mathematics
1st ed. 2017, VIII, 491 p. 13 illus.
Hardcover
ISBN 978-3-319-63229-2
* Written by an established authority in harmonic analysis of several complex variables
* Develops the harmonic analysis of several complex variables from the first principles
* Includes copious examples, explanations, and an exhaustive bibliography
* Contains several figures which illustrate the geometric nature of the subject
* Exercise sets at the end of each chapter are especially useful for graduate level students
Authored by a ranking authority in harmonic analysis of several complex variables, this
book embodies a state-of-the-art entree at the intersection of two important fields of
research: complex analysis and harmonic analysis. Written with the graduate student
in mind, it is assumed that the reader has familiarity with the basics of complex analysis
of one and several complex variables as well as with real and functional analysis. The
monograph is largely self-contained and develops the harmonic analysis of several
complex variables from the first principles. The text includes copious examples,
explanations, an exhaustive bibliography for further reading, and figures that illustrate
the geometric nature of the subject. Each chapter ends with an exercise set. Additionally,
each chapter begins with a prologue, introducing the reader to the subject matter that
follows; capsules presented in each section give perspective and a spirited launch to the
segment; preludes help put ideas into context. Mathematicians and researchers in several
applied disciplines will find the breadth and depth of the treatment of the subject highly
useful.
Series: Graduate Texts in Mathematics, Vol. 277
1st ed. 2017, X, 490 p. 6 illus.
Hardcover
ISBN 978-3-319-64545-2
* First book to present a complete and unified treatment of all parts
of the classical real moment problem (full and truncated, onedimensional and multidimensional)
* Develops classical and recent results with full proofs
* Contains new results and concepts on the truncated multidimensional moment problem
This advanced textbook provides a comprehensive and unified account of the moment
problem. It covers the classical one-dimensional theory and its multidimensional
generalization, including modern methods and recent developments.
In both the one-dimensional and multidimensional cases, the full and truncated moment
problems are carefully treated separately. Fundamental concepts, results and methods
are developed in detail and accompanied by numerous examples and exercises. Particular
attention is given to powerful modern techniques such as real algebraic geometry and
Hilbert space operators. A wide range of important aspects are covered, including the
Nevanlinna parametrization for indeterminate moment problems, canonical and principal
measures for truncated moment problems, the interplay between Positivstellensatze
and moment problems on semi-algebraic sets, the fibre theorem, multidimensional
determinacy theory, operator-theoretic approaches, and the existence theory and
important special topics of multidimensional truncated moment problems.
The Moment Problem will be particularly useful to graduate students and researchers
working on moment problems, functional analysis, complex analysis, harmonic analysis,
real algebraic geometry, polynomial optimization, or systems theory. With notes
providing useful background information and exercises of varying difficulty illustrating
the theory, this book will also serve as a reference on the subject and can be used for selfstudy.