Hardcover
ISBN 978-3-030-03073-5
Presents original research previously unpublished
Closes a gap in research
Develops quaternionic spectral theory
The subject of this monograph is the quaternionic spectral theory based on the notion of Sspectrum.
With the purpose of giving a systematic and self-contained treatment of this theory
that has been developed in the last decade, the book features topics like the S-functional
calculus, the F-functional calculus, the quaternionic spectral theorem, spectral integration and
spectral operators in the quaternionic setting. These topics are based on the notion of Sspectrum
of a quaternionic linear operator. Further developments of this theory lead to
applications in fractional diffusion and evolution problems that will be covered in a separate
monograph.
Hardcover
ISBN 978-3-030-04737-5
A novel approach to perturbative quantum field theory
Approach is conceptually clear, mathematically rigorous and pragmatically
useful for physicists
Presents mathematically stimulating discussions and physically interesting
formulations
The book develops a novel approach to perturbative quantum field theory: starting with a
perturbative formulation of classical field theory, quantization is done by deformation
quantization of the underlying free theory and by the principle that as much as possible from
the classical structure has to be maintained The resulting formulation of perturbative quantum
field theory is a version of Epstein-Glaser renormalization, which is conceptually clear,
mathematically rigorous and pragmatically useful for physicists. The connection to traditional
formulations of perturbative quantum field theory is worked out. The formalism is illustrated by
a lot of examples and exercises.
Hardcover
ISBN 978-3-030-02894-7
Presents a step-by-step guide for the techniques of basic functional
inequalities from the point of view of Folland and Stein's homogeneous (Lie)
groups, and for the applications of such methods. In addition, this book
shows that these methods sometimes give new results even in classical
(Euclidean) cases
Aims to collect the ideas underpinning Hardy type inequalities on general
homogeneous groups, in a way, accessible to anyone with a basic level of
understanding of analysis
Provides a self-contained coverage of elements of the traditional and modern
analysis on homogeneous Lie groups, and does not require a previous
background in Lie theory
Represents a detailed account of the rece
This open access book provides an extensive treatment of Hardy inequalities and closely
related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The
place where Hardy inequalities and homogeneous groups meet is a beautiful area of
mathematics with links to many other subjects. While describing the general theory of Hardy,
Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general
homogeneous groups, the authors pay particular attention to the special class of stratified
groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined
with the properties of sub-Laplacians and subelliptic partial differential equations. These topics
constitute the core of this book and they are complemented by additional, closely related
topics such as uncertainty principles, function spaces on homogeneous groups, the potential
theory for stratified groups, and the potential theory for general Hormander's sums of squares
and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i
Balaguer Prize, a prestigious award for books of expository nature presenting the latest
developments in an active area of research in mathematics.
Softcover
ISBN 978-3-030-01755-2
An excellent starting point for beginners in the field
An advanced high school student can learn basic concepts from the book
Gradual introduction of concepts with many figures and solved examples
A fresh look at the problems of modern theoretical physics
Comparison of standard mathematics to geometric algebra with examples
This book enables the reader to discover elementary concepts of geometric algebra and its
applications with lucid and direct explanations. Why would one want to explore geometric
algebra? What if there existed a universal mathematical language that allowed one: to make
rotations in any dimension with simple formulas, to see spinors or the Pauli matrices and their
products, to solve problems of the special theory of relativity in three-dimensional Euclidean
space, to formulate quantum mechanics without the imaginary unit, to easily solve difficult
problems of electromagnetism, to treat the Kepler problem with the formulas for a harmonic
oscillator, to eliminate unintuitive matrices and tensors, to unite many branches of
mathematical physics? What if it were possible to use that same framework to generalize the
complex numbers or fractals to any dimension, to play with geometry on a computer, as well
as to make calculations in robotics, ray-tracing and brain science? In addition, what if such a
language provided a clear, geometric interpretation of mathematical objects, even for the
imaginary unit in quantum mechanics? Such a mathematical language exists and it is called
geometric algebra. High school students have the potential to explore it, and undergraduate
students can master it. The universality, the clear geometric interpretation, the power of
generalizations to any dimension, the new insights into known theories, and the possibility of
computer implementations make geometric algebra a thrilling field to unearth.
Hardcover
ISBN 978-3-030-04305-6
First unified presentation of Fourier theory and corresponding algorithms
Covers many recent highly recognized developments in numerical Fourier
analysis
The code of most of the presented algorithms is available in public software
packages of the authors
This book offers a unified presentation of Fourier theory and corresponding algorithms
emerging from new developments in function approximation using Fourier methods. It starts
with a detailed discussion of classical Fourier theory to enable readers to grasp the
construction and analysis of advanced fast Fourier algorithms introduced in the second part,
such as nonequispaced and sparse FFTs in higher dimensions. Lastly, it contains a selection of
numerical applications, including recent research results on nonlinear function approximation
by exponential sums. The code of most of the presented algorithms is available in the authorsf
public domain software packages. Students and researchers alike benefit from this unified
presentation of Fourier theory and corresponding algorithms.
Hardcover
ISBN 978-3-030-03376-7
Combines uniquely deep abstract theory and the analysis of concrete
equations
Offers links to probability, control theory, game theory and interacting
particles
Exposes systematically the topic from its beginnings up to modern research
results
Introduces a new methodology of fast and unifying analysis of various
equations inspired by modern developments in fractional calculus and in the
theory of semigroups
Includes previously unpublished material
This advanced book focuses on ordinary differential equations (ODEs) in Banach and more
general locally convex spaces, most notably the ODEs on measures and various function
spaces. It briefly discusses the fundamentals before moving on to the cutting edge research in
linear and nonlinear partial and pseudo-differential equations, general kinetic equations and
fractional evolutions. The level of generality chosen is suitable for the study of the most
important nonlinear equations of mathematical physics, such as Boltzmann, Smoluchovskii,
Vlasov, Landau-Fokker-Planck, Cahn-Hilliard, Hamilton-Jacobi-Bellman, nonlinear Schroedinger,
McKean-Vlasov diffusions and their nonlocal extensions, mass-action-law kinetics from
chemistry. It also covers nonlinear evolutions arising in evolutionary biology and mean-field
games, optimization theory, epidemics and system biology, in general models of interacting
particles or agents describing splitting and merging, collisions and breakage, mutations and the
preferential-attachment growth on networks. The book is intended mainly for upper
undergraduate and graduate students, but is also of use to researchers in differential
equations and their applications.
Provides an extensive exploration of constant width bodies
Hardcover
ISBN 978-3-030-03866-3
Offers ample exercises that help readers understand specific topics within
convex geometry
Gives instructors a wealth of material to use in a convex geometry course
This is the first comprehensive monograph to thoroughly investigate constant width bodies,
which is a classic area of interest within convex geometry. It examines bodies of constant
width from several points of view, and, in doing so, shows surprising connections between
various areas of mathematics. Concise explanations and detailed proofs demonstrate the many
interesting properties and applications of these bodies. Numerous instructive diagrams are
provided throughout to illustrate these concepts. An introduction to convexity theory is first
provided, and the basic properties of constant width bodies are then presented. The book then
delves into a number of related topics, which include Constant width bodies in convexity
(sections and projections, complete and reduced sets, mixed volumes, and further partial fields)
Sets of constant width in non-Euclidean geometries (in real Banach spaces, and in hyperbolic,
spherical, and further non-Euclidean spaces) The concept of constant width in analysis (using
Fourier series, spherical integration, and other related methods) Sets of constant width in
differential geometry (using systems of lines and discussing notions like curvature, evolutes,
etc.) Bodies of constant width in topology (hyperspaces, transnormal manifolds, fiber bundles,
and related topics) The notion of constant width in discrete geometry (referring to geometric
inequalities, packings and coverings, etc.) Technical applications, such as film projectors, the
square-hole drill, and rotary engines Bodies of Constant Width: An Introduction to Convex
Geometry with Applications will be a valuable resource for graduate and advanced
undergraduate students studying convex geometry and related fields. Additionally, it will appeal
to any mathematicians with a general interest in geometry.
Hardcover
ISBN 978-3-030-04268-4
Celebrates Rien's many contributions to the field of operator theory during
more than fifty years
Contains biographical information on Rien Kaashoek
Comprises eighteen research papers by Rien's colleagues, collaborators,
students and friends
This volume is dedicated to Rien Kaashoek on the occasion of his 80th birthday and celebrates
his many contributions to thefield of operator theory during more than fifty years. In the first
part of the volume, biographical information and personal accounts on the life of Rien
Kaashoek are presented. Eighteen research papers by friends and colleagues of Rien Kaashoek
are included in the second part. Contributions by J. Agler, Z.A. Lykova, N.J. Young, J.A. Ball, G.J.
Groenewald, S. ter Horst, H. Bart, T. Ehrhardt, B. Silbermann, J.M. Bogoya, S.M. Grudsky, I.S.
Malysheva, A. Bottcher, E. Wegert, Z. Zhou, Y. Eidelman, I. Haimovici, A.E. Frazho, A.C.M. Ran, B.
Fritzsche, B. Kirstein, C.Madler, J. J. Jaftha, D.B. Janse van Rensburg, P. Junghanns, R. Kaiser, J.
Nemcova, M. Petreczky, J.H. van Schuppen, L. Plevnik, P. Semrl, A. Sakhnovich, F.-O. Speck, S.
Sremac, H.J. Woerdeman, H. Wolkowicz and N. Vasilevski.