Series: Birkhauser Advanced Texts Basler Lehrbucher
1st ed. 2019, Approx. 360 p.
Printed book
Hardcover
Entry point to Symplectic Field Theory (SFT)
Entry point for the study of finite energy foliations
Proves deep results in pseudoholomorphic curve theory
Written by leading researchers in this area
A must to have to graduate students entering this field of mathematical
research
This book explains the foundations of holomorphic curve theory in contact geometry. By using
a particular geometric problem as a starting point the authors guide the reader into the
subject. As such it ideally serves as preparation and as entry point for a deeper study of the
analysis underlying symplectic field theory.An introductory chapter sets the stage explaining
some of the basic notions of contact geometry and the role of holomorphic curves in the field.
The authors proceed to the heart of the material providing a detailed exposition about finite
energy planes and periodic orbits (chapter 4) to disk filling methods and applications (chapter
9). The material is self-contained. It includes a number of technical appendices giving the
geometric analysis foundations for the main results, so that one may easily follow the
discussion. Graduate students as well as researchers who want to learn the basics of this fast
developing theory will highly appreciate this accessible approach taken by the authors.
Series: PNLDE Subseries in Control
1st ed. 2019, XII, 204 p.
Printed book
Hardcover
Describes a new technique of stabilizing parabolic type equations
Discusses numerous applications for the control techniques presented
Will be an indispensable tool for researchers in control theory and engineers
from all fields
This monograph presents a technique, developed by the author, to design asymptotically
exponentially stabilizing finite-dimensional boundary proportional-type feedback controllers for
nonlinear parabolic-type equations. The potential control applications of this technique are wide
ranging in many research areas, such as Newtonian fluid flows modeled by the Navier-Stokes
equations; electrically conducted fluid flows; phase separation modeled by the Cahn-Hilliard
equations; and deterministic or stochastic semi-linear heat equations arising in biology,
chemistry, and population dynamics modeling. The text provides answers to the following
problems, which are of great practical importance: Designing the feedback law using a minimal
set of eigenfunctions of the linear operator obtained from the linearized equation around the
target state Designing observers for the considered control systems Constructing time-discrete
controllers requiring only partial knowledge of the state After reviewing standard notations and
results in functional analysis, linear algebra, probability theory and PDEs, the author describes
his novel stabilization algorithm. He then demonstrates how this abstract model can be applied
to stabilization problems involving magnetohydrodynamic equations, stochastic PDEs, nonsteadystates,
and more. Boundary Stabilization of Parabolic Equations will be of particular interest to
researchers in control theory and engineers whose work involves systems control. Familiarity
with linear algebra, operator theory, functional analysis, partial differential equations, and
stochastic partial differential equations is required.
Series: Monographs in Mathematics
1st ed. 2019, Approx. 500 p.
Printed book
Hardcover
Follows the steps of Vol. I "Abstract Linear Theory"
Features a clear and rigorous presentation style
Fills a gap in literature
This volume discusses an in-depth theory of function spaces in an Euclidean setting, including
several new features, not previously covered in the literature. In particular, it develops a unified
theory of anisotropic Besov and Bessel potential spaces on Euclidean corners, with infinitedimensional
Banach spaces as targets. It especially highlights the most important subclasses
of Besov spaces, namely Slobodeckii and Holder spaces. In this case, no restrictions are
imposed on the target spaces, except for reflexivity assumptions in duality results. In this
general setting, theauthorprovessharp embedding, interpolation, and trace theorems, point-wise
multiplier results, as well as Gagliardo-Nirenberg estimates and generalizations of Aubin-Lions
compactness theorems. The results presented pave the way for new applications in situations
where infinite-dimensional target spaces are relevant ? in the realm of stochastic differential
equations, for example
Series: International Series of Numerical Mathematics
1st ed. 2019, X, 136 p. 22 illus. in color.
Printed book
Hardcover
Highlights different aspects of nonsmooth and variational analysis
Presents optimization methods and their convergence theory and applications
Six research articles gathered focus on recent results
Since nonsmooth optimization problems arise in a diverse range of real-world applications, the
potential impact of efficient methods for solving such problems is undeniable. Even solving
difficult smooth problems sometimes requires the use of nonsmooth optimization methods, in
order to either reduce the problemfs scale or simplify its structure. Accordingly, the field of
nonsmooth optimization is an important area of mathematical programming that is based on
by now classical concepts of variational analysis and generalized derivatives, and has
developed a rich and sophisticated set of mathematical tools at the intersection of theory and
practice. This volume of ISNM is an outcome of the workshop "Nonsmooth Optimization and its
Applications," which was held from May 15 to 19, 2017 at the Hausdorff Center for
Mathematics, University of Bonn. The six research articles gathered here focus on recent results
that highlight different aspects of nonsmooth and variational analysis, optimization methods,
their convergence theory and applications.
Series: Operator Theory: Advances and Applications
1st ed. 2019, Approx. 300 p.
Printed book
Hardcover
Includes fourteen original research papers by friends and colleagues of Joe Ball
Honors the mathematical life of Joe Ball
Presents latest results in the fields of operator theory
This volume is devoted to Joseph A. (Joe) Ballfs contributions to operator theory and its
applications and in celebration of his seventieth birthday. Joe Ballfs career spans over four and
a half decades, starting with his work on model theory and related topics for non-contractions
and operators on multiply connected domains. Later on, more applied operator theory themes
appeared in his work, involving factorization and interpolation for operator-valued functions,
with extensive applications in system and control theory. He has worked on nonlinear control,
time-varying systems and, more recently, on multidimensional systems and noncommutative Htheory
on the unit ball and polydisk, and more general domains, and these are only the main
themes in his vast oeuvre. Fourteen research papers constitute the core of this volume, written
by mathematicians who have collaborated with Joe or have been influenced by his vast
mathematical work. A curriculum vitae, a publications list and a list of Joe Ballfs PhD students
are included in this volume, as well as personal reminiscences by colleagues and friends.
Contributions by Yu. M. Arlinskii, S. Hassi, M. Augat, J. W. Helton, I. Klep, S. McCullough, S.
Balasubramanian, U. Wijesooriya, N. Cohen, Q. Fang, S. Gorai, J. Sarkar, G. J. Groenewald, S. ter
Horst, J. Jaftha, A. C. M. Ran, M.A. Kaashoek, F. van Schagen, A. Kheifets, Z. A. Lykova, N. J.
Young, A. E. Ajibo, R. T. W. Martin, A. Ramanantoanina, M.-J. Y. Ou, H. J. Woerdeman, A. van der
Schaft, A. Tannenbaum, T. T. Georgiou, J. O. Deasy and L. Norton
Due 2019-06-29
1st ed. 2019, Approx. 230 p.
Printed book
Softcover
Includes research never published before in a book
Provides material suitable for graduate students
Gives an insightful overview on an active research area in complex analysis
This book presents the extensions to the quaternionic setting of some of the main
approximation results in complex analysis. It also includes the main inequalities regarding the
behavior of the derivatives of polynomials with quaternionic cofficients. With some few
exceptions, all the material in this book belongs to recent research of the authors on the
approximation of slice regular functions of a quaternionic variable. The book is addressed to
researchers in various areas of mathematical analysis, in particular hypercomplex analysis, and
approximation theory. It is accessible to graduate students and suitable for graduate courses in
the above framework.
Series: Pseudo-Differential Operators
1st ed. 2019, Approx. 500 p.
Printed book
Softcover
Presents new results of a classic field
Includes open problems
Describes recent developments on topics in non-self-adjoint operator theory
The asymptotic distribution of eigenvalues of self-adjoint differential operators in the highenergy
limit, or the semi-classical limit, is a classical subject going back to H. Weyl of more
than a century ago. In the last decades there has been a renewed interest in non-self-adjoint
differential operators which have many subtle properties such as instability under small
perturbations. Quite remarkably, when adding small random perturbations to such operators,
the eigenvalues tend to distribute according to Weyl's law (quite differently from the
distribution for the unperturbed operators in analytic cases). A first result in this direction was
obtained by M. Hager in her thesis of 2005. Since then, further general results have been
obtained, which are the main subject of the present book. Additional themes from the theory of
non-self-adjoint operators are also treated. The methods are very much based on microlocal
analysis and especially on pseudodifferential operators. The reader will find a broad field with
plenty of open problems