Softcover
ISBN 978-3-030-02265-5
Presents core material in spectral theory alongside several advanced topics
The first book entirely dedicated to the relationship between the various parts
of the spectrum
Self-contained collection of the most recent research on the topic
This monograph concerns the relationship between the local spectral theory and Fredholm
theory of bounded linear operators acting on Banach spaces. The purpose of this book is to
provide a first general treatment of the theory of operators for which Weyl-type or Browdertype
theorems hold. The product of intensive research carried out over the last ten years, this
book explores for the first time in a monograph form, results that were only previously
available in journal papers. Written in a simple style, with sections and chapters following an
easy, natural flow, it will be an invaluable resource for researchers in Operator Theory and
Functional Analysis. The reader is assumed to be familiar with the basic notions of linear
algebra, functional analysis and complex analysis.
Hardcover
ISBN 978-3-030-02912-8
Offers a detailed overview of the modern rank- and pseudo-rank-based
inference methodology
Richly illustrated with examples
Provides codes (R, SAS) for the statististical analysis
This book explains how to analyze independent data from factorial designs without having to
make restrictive assumptions, such asnormality of the data, or equal variances. The general
approach also allows for ordinal and even dichotomous data. The underlying effect size is the
nonparametric relative effect, which has a simple and intuitive probability interpretation. The
data analysis is presented as comprehensively as possible, including appropriate descriptive
statistics which follow a nonparametric paradigm, as well as corresponding inferential methods
using hypothesis tests and confidence intervals based on pseudo-ranks. Offering clear
explanations, an overview of the modern rank- and pseudo-rank-based inference methodology
and numerous illustrations with real data examples, as well as the necessary R/SAS code to
run the statistical analyses, this book is a valuable resource for statisticians and practitioners
alike.
Hardcover
ISBN 978-3-030-02942-5
Leads a reader to far advanced topics widely used in modern research, using
basic tools from the first two years of university studies
From the very beginning, the study of algebraic curves is aimed at the
construction of their moduli spaces in the final chapters
Supplied with numerous exercises and problems both making the book a
convenient base for a university lecture course and allowing the reader to
control his/her progress
This book offers a concise yet thorough introduction to the notion of moduli spaces of complex
algebraic curves. Over the last few decades, this notion has become central not only in
algebraic geometry, but in mathematical physics, including string theory, as well. The book
begins by studying individual smooth algebraic curves, including the most beautiful ones,
before addressing families of curves. Studying families of algebraic curves often proves to be
more efficient than studying individual curves: these families and their total spaces can still be
smooth, even if there are singular curves among their members. A major discovery of the 20th
century, attributed to P. Deligne and D. Mumford, was that curves with only mild singularities
form smooth compact moduli spaces. An unexpected byproduct of this discovery was the
realization that the analysis of more complex curve singularities is not a necessary step in
understanding the geometry of the moduli spaces. The book does not use the sophisticated
machinery of modern algebraic geometry, and most classical objects related to curves ? such
as Jacobian, space of holomorphic differentials, the Riemann-Roch theorem, and Weierstrass
points ? are treated at a basic level that does not require a profound command of algebraic
geometry, but which is sufficient for extending them to vector bundles and other geometric
objects associated to moduli spaces. Nevertheless, it offers clear information on the
construction of the moduli spaces, and provides readers with tools for practical operations with
this notion.
Hardcover
ISBN 978-981-13-2594-6
Discusses about the fundamentals of wavelet theory and its applications
Maintains a balance between mathematical rigour and practical applications
of wavelet theory
Uses the remarks and graphical representations to explain mathematical
ideas in a conversational way
Applies MATLAB to solve numerical examples
This book provides comprehensive information on the conceptual basis of wavelet theory and it
applications. Maintaining an essential balance between mathematical rigour and the practical
applications of wavelet theory, the book is closely linked to the wavelet MATLAB toolbox, which
is accompanied, wherever applicable, by relevant MATLAB codes. The book is divided into four
parts, the first of which is devoted to the mathematical foundations. The second part offers a
basic introduction to wavelets. The third part discusses wavelet-based numerical methods for
differential equations, while the last part highlights applications of wavelets in other fields. The
book is ideally suited as a text for undergraduate and graduate students of mathematics and
engineering.
Softcover
ISBN 978-3-030-03295-1
Pursues the development of distribution theory simultaneously with relevant
incursions into partial differential equations and harmonic analysis
Written in a concise, rigorous, and largely self-contained form with a balanced
treatment of the topics involved
Equips readers to handle subsequent courses dealing with allied topics,
including: Harmonic Analysis, Partial Differential Equations, Boundary
Integral Methods, Sobolev Spaces, Pseudodifferential Operators
The aim of this book is to offer, in a concise, rigorous, and largely self-contained manner, a
rapid introduction to the theory of distributions and its applications to partial differential
equations and harmonic analysis. The book is written in a format suitable for a graduate
course spanning either over one-semester, when the focus is primarily on the foundational
aspects, or over a two-semester period that allows for the proper amount of time to cover all
intended applications as well. It presents a balanced treatment of the topics involved, and
contains a large number of exercises (upwards of two hundred, more than half of which are
accompanied by solutions), which have been carefully chosen to amplify the effect, and
substantiate the power and scope, of the theory of distributions. Graduate students,
professional mathematicians, and scientifically trained people with a wide spectrum of
mathematical interests will find this book to be a useful resource and complete self-study
guide.
Hardcover
ISBN 978-3-030-03753-6
Reports on the progress in the theory of algebraic numbers in the first half of
the 20th century
Offers a unique opportunity of looking at this development at all levels,
including its small steps performed by people now unknown
May prevent rediscoveries of old results and may induce researchers to find
new applications of ideas hidden in the old literature
The book is aimed at people working in number theory or at least interested in this part of
mathematics. It presents the development of the theory of algebraic numbers up to the year
1950 and contains a rather complete bibliography of that period. The reader will get
information about results obtained before 1950. It is hoped that this may be helpful in
preventing rediscoveries of old results, and might also inspire the reader to look at the work
done earlier, which may hide some ideas which could be applied in contemporary research.
Hardcover
ISBN 978-3-030-01811-5
Self-contained introduction to signal processing and wavelets assuming only
a linear algebra background
Hands-on introduction to important concepts using computational and
interactive examples and exercises
Strong rooting of the developed theory in terms of practical applications to
sound and images
This book offers a user friendly, hands-on, and systematic introduction to applied and
computational harmonic analysis: to Fourier analysis, signal processing and wavelets; and to
their interplay and applications. The approach is novel, and the book can be used in
undergraduate courses, for example, following a first course in linear algebra, but is also
suitable for use in graduate level courses. The book will benefit anyone with a basic
background in linear algebra. It defines fundamental concepts in signal processing and wavelet
theory, assuming only a familiarity with elementary linear algebra. No background in signal
processing is needed. Additionally, the book demonstrates in detail why linear algebra is often
the best way to go. Those with only a signal processing background are also introduced to the
world of linear algebra, although a full course is recommended. The book comes in two
versions: one based on MATLAB, and one on Python, demonstrating the feasibility and
applications of both approaches. Most of the MATLAB code is available interactively. The
applications mainly involve sound and images. The book also includes a rich set of exercises,
many of which are of a computational nature.