Discusses major topics in the spectral theory of dynamical systems
Includes two advanced theorems: a theorem by Helson and Parry, and B. Host’s theorem
Features a new chapter on “Calculus of Generalized Riesz Products”
Describes Ornstein’s family of mixing rank-one automorphisms with construction and proof
Explains systems of imprimitivity and their relevance to ergodic theory, aswell as Baire category theorems
This book discusses basic topics in the spectral theory of dynamical systems, including two
advanced theorems by H. Helson, W. Parry, and B. Host. It goes on to describe the Ornstein’s
family of mixing rank-one automorphisms with construction and proof. Systems of imprimitivity
and their relevance to ergodic theory are also examined. The book also discusses Baire
category theorems of ergodic theory, scattered in literature, in a unified way. Riesz products are
considered and used to describe the spectral types and eigenvalues of rank-one
automorphisms. This second edition of the book includes a new chapter “Calculus of
Generalized Riesz Products”, which discusses the recent work connecting generalized Riesz
products, Hardy classes, Banach's problem of simple Lebesgue spectrum in ergodic theory, and
flat polynomials
Due 2020-09-07
1st ed. 2020, XIII, 223 p.
Hardcover
ISBN 978-981-15-6224-2
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Science (SC)
Product category : Monograph
Mathematics : Dynamical Systems and Ergodic Theory
Series : Texts and Readings in Mathematics
Features compact and clearly presented proofs
Focuses on approximation theory, providing the key concepts needed to grasp the subject matter
Highlighting classic approximation results but also new work, it represents an
important contribution to the area of approximation theory
This book presents the evolution of uniform approximations of continuous functions. Starting
from the simple case of a real continuous function defined on a closed real interval, i.e., the
Weierstrass approximation theorems, it proceeds up to the abstract case of approximation
theorems in a locally convex lattice of (M) type. The most important generalizations of
Weierstrass’ theorems obtained by Korovkin, Bohman, Stone, Bishop, and Von Neumann are
also included. In turn, the book presents the approximation of continuous functions defined on
a locally compact space (the functions from a weighted space) and that of continuous
differentiable functions defined on¡n. In closing, it highlights selected approximation theorems
in locally convex lattices of (M) type. The book is intended for advanced and graduate students
of mathematics, and can also serve as a resource for researchers in the field of the theory of
functions.
Due 2020-09-12
1st ed. 2020, X, 140 p. 1
illus. in color.
Softcover
ISBN 978-3-030-48411-8
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Science (SC)
Product category : Monograph
Series : Frontiers in Mathematics
Mathematics : Functional Analysis
Presents the essence of the theory on smooth manifolds
Covers key topics such as submanifolds, tensor fields, Lie groups, integration
(including Stokes’ theorem and De Rham cohomology), as well as manifolds
Includes comprehension exercises throughout the text and challenging
problems at the end of each chapter
This concise and practical textbook presents the essence of the theory on smooth manifolds. A
key concept in mathematics, smooth manifolds are ubiquitous: They appear as Riemannian
manifolds in differential geometry; as space-times in general relativity; as phase spaces and
energy levels in mechanics; as domains of definition of ODEs in dynamical systems; as Lie
groups in algebra and geometry; and in many other areas. The book first presents the
language of smooth manifolds, culminating with the Frobenius theorem, before discussing the
language of tensors (which includes a presentation of the exterior derivative of differential
forms). It then covers Lie groups and Lie algebras, briefly addressing homogeneous manifolds.
Integration on manifolds, explanations of Stokes’ theorem and de Rham cohomology, and
rudiments of differential topology complete this work. It also includes exercises throughout the
text to help readers grasp the theory, as well as more advanced problems for challengeoriented minds at the end of each chapter.
Conceived for a one-semester course on
Differentiable Manifolds and Lie Groups, which is offered by many graduate programs
worldwide, it is a valuable resource for students and lecturers alike
Due 2020-09-12
1st ed. 2020, XII, 154 p. 11
illus.
Softcover
ISBN 978-3-030-49774-3
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Standard (0)
Product category : Graduate/advanced undergraduate textbook
Series : Compact Textbooks in Mathematics
Mathematics : Global Analysis and Analysis on Manifolds
Configural Frequency Analysis (CFA) and Other Methods for the Analysis
of Contingency Tables
Series: SpringerBriefs in Statistics
Features an electronic supplement with 18 R-scripts and many datasets, so
that readers can familiarize themselvs with R package confreq
Teaches statistical methods in an approachable format for scholars in the
Social Sciences
Includes software demonstrations with open source software package R that
is available through CRAN
This book offers a comprehensible overview of the statistical approach called the personcentered method.
Instead of analyzing means, variances and covariances of scale scores as in
the common variable-centered approach, the person-centered approach analyzes persons or
objects grouped according to their characteristic patterns or configurations in contingency
tables. This second edition explores the relationship between two statistical methods: log-linear
modeling (LLM) and configural frequency analysis (CFA). Both methods compare expected
frequencies with observed frequencies. However, while LLM searches for the underlying
dependencies of the involved variables in the data (model-fitting), CFA examines significant
residuals in non-fitting models. New developments in the second edition include: Configural
Mediation Models, CFA with covariates, moderator CFA, and CFA modeling branches in treebased methods.
The new developments enable the use of categorical together with continuous
variables, which makes CFA a very powerful statistical tool. This new edition continues to utilize
R-packageconfreq (derived from Configural Frequency Analysis), much updated since the first
edition and newly adjusted to the new R base program 4.0. An electronic supplement is now
available with 18 R-scripts and many datasets.
2nd ed. 2020, X, 116 p. 29 illus., 5 illus. in color.
Mathematics : Global Analysis and Analysis on Manifolds
Reflects the most recent developments in the field
The exposition is entirely self-contained
Provides detailed proofs preceded by outlines for the convenience of the reader
This self-contained book lays the foundations for a systematic understanding of potential
theoretic and uniformization problems on fractal Sierpiski carpets, and proposes a theory based
on the latest developments in the field of analysis on metric spaces. The first part focuses on
the development of an innovative theory of harmonic functions that is suitable for Sierpiski
carpets but differs from the classical approach of potential theory in metric spaces. The second
part describes how this theory is utilized to prove a uniformization result for Sierpiski carpets.
This book is intended for researchers in the fields of potential theory, quasiconformal
geometry, geometric group theory, complex dynamics, geometric function theory and PDEs
Due 2020-10-02
1st ed. 2020, X, 186 p. 10
illus., 4 illus. in color.
Softcover
ISBN 978-3-030-50804-3
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Product category : Monograph
Series : Lecture Notes in Mathematics
Mathematics : Functions of a Complex Variable
Hyperbolicity in Montréal
Introduces a number of exciting developments and cutting-edge results
related to hyperbolicity, and the fundamental conjectures of Ax–Schanuel,
Bombieri, Campana, Lang, Vojta, and others
Features chapters written by leading experts in their areas, collecting many of
their own recent advances
Motivates a range of readers by presenting each chapter’s respective material
in a self-contained and accessible manner
This textbook introduces exciting new developments and cutting-edge results on the theme of
hyperbolicity. Written by leading experts in their respective fields, the chapters stem from minicourses
given alongside three workshops that took place in Montréal between 2018 and 2019.
Each chapter is self-contained, including an overview of preliminaries for each respective topic.
This approach captures the spirit of the original lectures, which prepared graduate students
and those new to the field for the technical talks in the program. The four chapters turn the
spotlight on the following pivotal themes: The basic notions of o-minimal geometry, which
build to the proof of the Ax–Schanuel conjecture for variations of Hodge structures; A broad
introduction to the theory of orbifold pairs and Campana's conjectures, with a special emphasis
on the arithmetic perspective; A systematic presentation and comparison between different
notions of hyperbolicity, as an introduction to the Lang–Vojta conjectures in the projective case;
An exploration of hyperbolicity and the Lang–Vojta conjectures in the general case of quasiprojective varieties.
Due 2020-10-03
1st ed. 2020, III, 221 p. 25
illus., 6 illus. in color.
ISBN 978-3-030-49863-4
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Product category : Graduate/advanced undergraduate textbook
Series : CRM Short Courses
Mathematics : Algebraic Geometry