Series: Springer Proceedings in Mathematics & Statistics, Vol. 206
1st ed. 2017, VI, 335 p. 2 illus.
Hardcover
ISBN 978-981-10-6118-9
* Features original works and survey articles on topics of function
spaces and inequalities
* Discusses recent developments in the theory of spaces with variable
exponents
* Presents papers on topics from Lebesgue spaces, Orlicz spaces,
Lorentz spaces and Morrey spaces
* Includes papers on further investigations concern Sobolev-type
embeddings, discrete inequalities and harmonic analysis
This book features original research and survey articles on the topics of function spaces
and inequalities. It focuses on (variable/grand/small) Lebesgue spaces, Orlicz spaces,
Lorentz spaces, and Morrey spaces and deals with mapping properties of operators,
(weighted) inequalities, pointwise multipliers and interpolation. Moreover, it considers
Sobolev*Besov and Triebel*Lizorkin type smoothness spaces. The book includes papers
by leading international researchers, presented at the International Conference on
Function Spaces and Inequalities, held at the South Asian University, New Delhi, India, on
11*15 December 2015, which focused on recent developments in the theory of spaces
with variable exponents. It also offers further investigations concerning Sobolev-type
embeddings, discrete inequalities and harmonic analysis. Each chapter is dedicated to a
specific topic and written by leading experts, providing an overview of the subject and
stimulating future research.
Series: Springer Proceedings in Mathematics & Statistics, Vol. 211
1st ed. 2017, IX, 236 p. 14 illus., 8 illus. in color.
Hardcover
ISBN 978-3-319-66289-3
This volume contains a collection of research papers and useful surveys by experts in
the field which provide a representative picture of the current status of this fascinating
area. Based on contributions from the VIII International Meeting on Lorentzian Geometry,
held at the University of Malaga, Spain, this volume covers topics such as distinguished
(maximal, trapped, null, spacelike, constant mean curvature, umbilical...) submanifolds,
causal completion of spacetimes, stationary regions and horizons in spacetimes, solitons
in semi-Riemannian manifolds, relation between Lorentzian and Finslerian geometries
and the oscillator spacetime.
In the last decades Lorentzian geometry has experienced a significant impulse, which
has transformed it from just a mathematical tool for general relativity to a consolidated
branch of differential geometry, interesting in and of itself. Nowadays, this field provides a
framework where many different mathematical techniques arise with applic
ations to multiple parts of mathematics and physics. This book is addressed to differential
geometers, mathematical physicists and relativists, and graduate students interested in
the field.
Series: Applied and Numerical Harmonic Analysis
1st ed. 2017, XIX, 343 p. 32 illus.
A product of Birkhauser Basel
Hardcover
ISBN 978-3-319-65321-1
* Aimed at students who have a basic knowledge of undergraduate
real analysis. All of the required background material is reviewed in
the first chapter
* Suitable for undergraduate-level courses; no familiarity with
measure theory is required
* Extensive exercises complement the text and provide opportunities
for learning by doing
* A separate solutions manual is available for instructors via the
Birkhauser website (www.springer.com/978-3-319-65321-1)
* Unique text providing an undergraduate-level introduction to
metrics, norms, inner products, and their associated operator theory
This text is a self-contained introduction to the three main families that we encounter
in analysis * metric spaces, normed spaces, and inner product spaces * and to the
operators that transform objects in one into objects in another. With an emphasis on
the fundamental properties defining the spaces, this book guides readers to a deeper
understanding of analysis and an appreciation of the field as the gscience of functions.h
Many important topics that are rarely presented in an accessible way to undergraduate
students are included, such as unconditional convergence of series, Schauder bases for
Banach spaces, the dual of *p topological isomorphisms, the Spectral Theorem, the Baire
Category Theorem, and the Uniform Boundedness Principle. The text is constructed in
such a way that instructors have the option whether to include more advanced topics.
Written in an appealing and accessible style
, Metrics, Norms, Inner Products, and Operator Theory is suitable for independent study
or as the basis for an undergraduate-level course. Instructors have several options for
building a course around the text depending on the level and interests of their students.
* Aimed at students who have a basic knowledge of undergraduate real analysis.
Series: Developments in Mathematics, Vol. 51
1st ed. 2017, XIV, 269 p.
Hardcover
ISBN 978-981-10-6655-9
* Systematically presents topological theory and dynamics for
evolution inclusions, together with relevant applications
* Covers evolution inclusions with m-dissipative operators, with the
Hille-Yosida operator, with time delay, and with impulses, as well as
stochastic evolution inclusions
* Fills an important gap in the body of literature on the topological
theory and dynamics of evolution inclusions and their applications
This book systematically presents the topological structure of solution sets and
attractability for nonlinear evolution inclusions, together with its relevant applications in
control problems and partial differential equations. It provides readers the background
material needed to delve deeper into the subject and explore the rich research literature.
In addition, the book addresses many of the basic techniques and results recently
developed in connection with this theory, including the structure of solution sets
for evolution inclusions with m-dissipative operators; quasi-autonomous and nonautonomous
evolution inclusions and control systems;evolution inclusions with the Hille-
Yosida operator; functional evolution inclusions; impulsive evolution inclusions; and
stochastic evolution inclusions. Several applications of evolution inclusions and control
systems are also discussed in detail.
Based on extensive research work conducted by the authors and other experts over the
past four years, the information presented is cutting-edge and comprehensive. As such,
the book fills an important gap in the body of literature on the structure of evolution
inclusions and its applications.
Series: Probability Theory and Stochastic Modelling, Vol. 85
1st ed. 2017, XVII, 250 p. 21 illus. in color.
Hardcover
ISBN 978-981-10-6264-3
* Makes recent results on the derivation of higher order numerical
schemes for random ordinary differential equations (RODEs)
available to a broader readership
* Develops numerical methods for random ODEs (RODEs)
* Highlights important applications, with a focus on dynamical
behavior and the biological sciences
This book is intended to make recent results on the derivation of higher order numerical
schemes for random ordinary differential equations (RODEs) available to a broader
readership, and to familiarize readers with RODEs themselves as well as the closely
associated theory of random dynamical systems. In addition, it demonstrates how RODEs
are being used in the biological sciences, where non-Gaussian and bounded noise are
often more realistic than the Gaussian white noise in stochastic differential equations
(SODEs).
RODEs are used in many important applications and play a fundamental role in the
theory of random dynamical systems. They can be analyzed pathwise with deterministic
calculus, but require further treatment beyond that of classical ODE theory due to the
lack of smoothness in their time variable. Although classical numerical schemes for
ODEs can be used pathwise for RODEs, they rarely attain their traditional order since the
solutions of RODEs do not have sufficient smoothness to have Taylor expansions in the
usual sense. However, Taylor-like expansions can be derived for RODEs using an iterated
application of the appropriate chain rule in integral form, and represent the starting point
for the systematic derivation of consistent higher order numerical schemes for RODEs.
The book is directed at a wide range of readers in applied and computational
mathematics and related areas as well as readers who are interested in the applications of
mathematical models involving random effects, in particular in the biological sciences.The
level of this book is suitable for graduate students in applied mathematics and related
areas, computational sciences and systems biology. A basic knowledge of ordinary
differential equations and numerical analysis is required.