Due 2019-10-18
1st ed. 2019, XXIX, 483 p. 5
illus.
Printed book
Hardcover
ISBN 978-3-030-27091-9
First book on the applications of logic and set theory to operator algebras
Presents dramatic progress on the resolution of several long-standing
problems on C*-algebras
Provides a concise guide to the relevant theory of sets and C*-algebras
This book explores and highlights the fertile interaction between logic and operator algebras,
which in recent years has led to the resolution of several long-standing open problems on C*-
algebras. The interplay between logic and operator algebras (C*-algebras, in particular) is
relatively young and the author is at the forefront of this interaction. The deep level of
scholarship contained in these pages is evident and opens doors to operator algebraists
interested in learning about the set-theoretic methods relevant to their field, as well as to settheorists
interested in expanding their view to the non-commutative realm of operator algebras.
Enough background is included from both subjects to make the book a convenient, selfcontained
source for students. A fair number of the exercises form an integral part of the text.
They are chosen to widen and deepen the material from the corresponding chapters. Some
other exercises serve as a warmup for the latter chapters.
Due 2019-10-20
1st ed. 2019, VIII, 326 p. 4
illus.
Printed book
Softcover
ISBN 978-3-030-27389-7
Offers a new, easier-to-grasp approach on the Kolmogorov-Bernoulli equivalence
Uses a myriad of tools, like the Lyapunov exponent and Pesinfs theory, to
present the KB equivalence in other frameworks
Includes a survey of recent results in the field
This book offers an introduction to a classical problem in ergodic theory and smooth dynamics,
namely, the Kolmogorov?Bernoulli(non)equivalence problem, and presents recent results in this
field. Starting with a crash course on ergodic theory, it uses the class of ergodic
automorphisms of the two tori as a toy model to explain the main ideas and technicalities
arising in the aforementioned problem. The level of generality then increases step by step,
extending the results to the class of uniformly hyperbolic diffeomorphisms, and concludes with
a survey of more recent results in the area concerning, for example, the class of partially
hyperbolic diffeomorphisms. It is hoped that with this type of presentation, nonspecialists and
young researchers in dynamical systems may be encouraged to pursue problems in this area.
Due 2019-10-26
1st ed. 2019, II, 122 p.
Printed book
Softcover
ISBN 978-3-030-29267-6
Enriches understanding of Hilbert-type inequalities
Presents recent developments and new results
Uses constant factors to extended Hurwitz zeta function with examples
This book is aimed toward graduate students and researchers in mathematics, physics and
engineering interested in the latest developments in analytic inequalities, Hilbert-Type and
Hardy-Type integral inequalities, and their applications. Theories, methods, and techniques of
real analysis and functional analysis are applied to equivalent formulations of Hilbert-type
inequalities, Hardy-type integral inequalities as well as their parameterized reverses. Special
cases of these integral inequalities across an entire plane are considered and explained.
Operator expressions with the norm and some particular analytic inequalities are detailed
through several lemmas and theorems to provide an extensive account of inequalities and
operators.
Due 2019-10-22
1st ed. 2019, IX, 251 p. 8
illus.
Printed book
Hardcover
ISBN 978-981-13-9848-3
Discusses the fundamental topics in Galois theory and advanced linear algebra
Serves as an easy-to-understand textbook for undergraduate students of linear algebra
Helps students understand other courses, such as Riemannian geometry
This book discusses major topics in Galois theory and advanced linear algebra, including
canonical forms. Divided into four chapters and presenting numerous new theorems, it serves
as an easy-to-understand textbook for undergraduate students of advanced linear algebra, and
helps students understand other courses, such as Riemannian geometry. The book also
discusses key topics including Cayley?Hamilton theorem, Galois groups, Sylvesterfs law of
inertia, Eisenstein criterion, and solvability by radicals. Readers are assumed to have a grasp of
elementary properties of groups, rings, fields, and vector spaces, and familiarity with the
elementary properties of positive integers, inner product space of finite dimension and linear
transformations is beneficial.
Due 2019-10-19
1st ed. 2019, VIII, 226 p.
72 illus., 62 illus. in color.
Printed book
Hardcover
ISBN 978-3-030-27330-9
Gathers selected contributions on computer aided geometric design and
isogeometric analysis
Presents theoretical and computational aspects of advanced geometric and
numerical methods
Includes state-of-the-art surveys on prominent research topics in the field
This book gathers selected contributions presented at the INdAM Workshop gDREAMSh, held in
Rome, Italy on January 2226, 2018. Addressing cutting-edge research topics and advances in
computer aided geometric design and isogeometric analysis, it covers distinguishing curve
/surface constructions and spline models, with a special focus on emerging adaptive spline
constructions, fundamental spline theory and related algorithms, as well as various aspects of
isogeometric methods, e.g. efficient quadrature rules and spectral analysis for isogeometric Bspline
discretizations. Applications in finite element and boundary element methods are also
discussed. Given its scope, the book will be of interest to both researchers and graduate
students working in these areas.
Due 2019-10-25
1st ed. 2019, XVI, 136 p. 14
illus.
Printed book
Softcover
ISBN 978-981-32-9304-5
Is a comprehensive survey of recent results of the existence of ground states
of models in quantum field theory
Focuses on non-perturbative methods, independent of coupling constants and
other factors
Begins with fundamentals of quantum field theory and takes the reader to a
higher level of appreciation of that theory
This book provides self-contained proofs of the existence of ground states of several
interaction models in quantum field theory. Interaction models discussed here include the spinboson
model, the Nelson model with and without an ultraviolet cutoff, and the Pauli?Fierz
model with and without dipole approximation in non-relativistic quantum electrodynamics.
These models describe interactions between bose fields and quantum mechanical matters. A
ground state is defined as the eigenvector associated with the bottom of the spectrum of a selfadjoint
operator describing the Hamiltonian of a model. The bottom of the spectrum is however
embedded in the continuum and then it is non-trivial to show the existence of ground states in
non-perturbative ways. We show the existence of the ground state of the Pauli?Fierz mode, the
Nelson model, and the spin-boson model, and several kinds of proofs of the existence of
ground states are explicitly provided. Key ingredients are compact sets and compact operators
in Hilbert spaces. For the Nelson model with an ultraviolet cutoff and the Pauli?Fierz model
with dipole approximation we show not only the existence of ground states but also enhanced
binding. The enhanced binding means that a system for zero-coupling has no ground state but
it has a ground state after turning on an interaction. The book will be of interest to graduate
students of mathematics as well as to students of the natural sciences who want to learn
quantum field theory from a mathematical point of view. It begins with abstract compactness
arguments in Hilbert spaces and definitions of fundamental facts of quantum field theory:
boson Fock spaces, creation operators, annihilation operators, and second quantization.
Due 2019-10-27
1st ed. 2019, XII, 196 p. 1
illus. in color.
Printed book
Hardcover
ISBN 978-3-030-26561-8
Covers a wide range of the groups with minute descriptions for harmonic
analysis, including both semi-simple Lie groups and solvable Lie groups
Includes hot topics presented at the 5 Tunisian-Japanese conference th
Features peer-reviewed contributions
This book presents a number of important contributions focusing on harmonic analysis and
representation theory of Lie groups. All were originally presented at the 5th Tunisian?Japanese
conference gGeometric and Harmonic Analysis on Homogeneous Spaces and Applicationsh,
which was held at Mahdia in Tunisia from 17 to 21 December 2017 and was dedicated to the
memory of the brilliant Tunisian mathematician Majdi Ben Halima.The peer-reviewed
contributions selected for publication have been modified and are, without exception, of a
standard equivalent to that in leading mathematical periodicals.Highlighting the close links
between group representation theory and harmonic analysis on homogeneous spaces and
numerous mathematical areas, such as number theory, algebraic geometry, differential
geometry, operator algebra, partial differential equations and mathematical physics, the book is
intended for researchers and students working in the area of commutative and noncommutative
harmonic analysis as well as group representations.