Bottcher, Albrecht, Silbermann, Bernd
Analysis of Toeplitz Operators, 2nd ed.
Series: Springer Monographs in Mathematics
2006, Approx. 675 p. 15 illus., Hardcover
ISBN: 3-540-32434-8
About this book
Toeplitz operators arise in plenty of applications. They
constitute one of the most important classes of non-selfadjoint
operators, and the ideas and methods prevailing in the field of
Toeplitz operators are a fascinating illustration of the fruitful
interplay between operator theory, complex analysis, and Banach
algebra techniques. This book is a systematic introduction to the
advanced analysis of block Toeplitz operators and includes both
classical results and recent developments.
Its first edition has been a standard reference for fifteen years.
The present second edition is enriched by several results
obtained only in the last decade. The topics treated range from
the analysis of locally sectorial matrix functions through
Toeplitz and Wiener-Hopf operators on Banach spaces, projection
methods, and quarter-plane operators up to Toeplitz and Wiener-Hopf
determinants.
The book is addressed to both graduate students approaching the
subject for the first time and specialists in the theory of
Toeplitz operators, but should also be of interest to physicists,
probabilists, and computer scientists.
Written for:
Researchers and graduate students
Table of contents
Auxiliary material.- Basic theory.- Symbol analysis.- Toeplitz
operators on H2.- Toeplitz operators on Hp.- Toeplitz operators
on Lp.- Finite section method.- Toeplitz operators over the
quarter-plane.- Wiener-Hopf integral operators.- Toeplitz
determinants.
Cid, Carlos, Murphy, Sean, Robshaw, Matthew
Algebraic Aspects of the Advanced Encryption Standard
2006, Approx. 125 p. 50 illus., Hardcover
ISBN: 0-387-24363-1
About this book
The Belgian block cipher Rijndael was chosen in 2000 by the U.S.
government’s National Institute of Standards and Technology (NIST)
to be the successor to the Data Encryption Standard. Rijndael was
subsequently standardised as the Advanced Encryption Standard (AES),
which is potentially the world’s most important block cipher.
In 2002, some new analytical techniques were suggested that may
have a dramatic effect on the security of the AES. Existing
analytical techniques for block ciphers depend heavily on a
statistical approach, whereas these new techniques are algebraic
in nature.
Algebraic Aspects of the Advanced Encryption Standard, appearing
five years after publication of the AES, presents the state of
the art for the use of such algebraic techniques in analysing the
AES.
The primary audience for this work includes academic and industry
researchers in cryptology; the book is also suitable for advanced-level
students.
Written for:
Industry and academic researchers in cryptology and security
Table of contents
The Advanced Encryption Standard (AES) - History, Design,
Traditional Attacks.- Mathematical Background.- Fields,
Commutative Algebra, Groebner Bases.- Alternative Representations
of the AES - Schroeppel, Book of Rijndaels, Dual Rijndaels.- AES
Equation Systems.- AES Systems over Binary Field GF(2), BES
Systems.- Methods of Analysis.- Equation Solving, Geometric
Approaches and Other Ongoing Work.- Summary of the Latest
Research.
Furht, Borko (Ed.)
Encyclopedia of Multimedia
2006, XXVIII, 989 p. 300 illus., Hardcover
ISBN: 0-387-24395-X
About this book
The Encyclopedia of Multimedia provides easily accessible
coverage of the important concepts, issues and technology trends
in the field of multimedia technologies, systems, techniques, and
applications. It is a comprehensive collection of more than 250
entries from hundreds of leading researchers and world experts.
With over 1000 heavily-illustrated pages, the Encyclopedia of
Multimedia presents concise overviews of all aspects of software,
systems, web tools and hardware that enable video, audio and
developing media to be shared and delivered electronically.
The Editor-in-Chief, Borko Furht, in collaboration with an
Editorial Board, surveyed and divided the field of multimedia
into specific topics that collectively encompass the foundations,
technologies, applications, and emerging elements behind web
technologies, wireless information transfer, and audio-visual
formatting and storage. Borko Furht is also the Founder and
Editor-in-Chief of the international journal, Multimedia Tools
and Applications.
The intended audience of the Encyclopedia of Multimedia is
technically diverse and wide; it includes professionals concerned
with the internet, websites, telecommunications, multimedia
players and technologies. Specifically, this volume serves as a
valuable reference for system designers, software engineers,
programmers, and business managers who are involved in multimedia
system design and their applications. Practitioners in
communications and software industries will benefit from this
reference, as will advanced-level students in computer science,
web design, and electrical engineering.
Written for:
University libraries, multimedia industry professionals, advanced-level
students
Table of contents
Szekelyhidi, Laszlo
Discrete Spectral Synthesis and Its Applications
Series: Springer Monographs in Mathematics
2006, Approx. 115 p., Hardcover
ISBN: 1-4020-4636-7
About this book
Spectral analysis and spectral synthesis deal with the
description of translation invariant function spaces over locally
compact Abelian groups. Translation invariant function spaces
appear in several different contexts for example linear ordinary
and partial difference and differential equations with constant
coefficients, theory of group representations, classical theory
of functional equations.
A fundamental problem is to discover the structure of such spaces
of functions, or more exactly, to find an appropriate class of
basic functions, the building blocks, which serve as "typical
elements" of the space, a kind of basis. It turns out that
these building blocks are the exponential monomials.
The problem of spectral analysis is if the function spaces in
question contain any exponential monomials. However, the problem
of spectral synthesis is in ascertaining if there are enough
exponential monomials in these function spaces to span a dense
subspace.
This book studies the situation over discrete Abelian groups with
wide range applications in the fields of classical functional
equations, difference and differential equations, polynomial
ideals, digital filtering and polynomial hypergroups.
Written for:
Graduate students, research workers in harmonic analysis,
spectral analysis, functional equations and hypergroups
Table of contents
Preface.- Introduction.- Spectral Synthesis and Spectral Analysis.-
Spectral Analysis and Spectral Synthesis on Discrete Abelian
Groups.- Spectral Synthesis and Functional Equations.- Mean
Periodic Functions.- Difference Equations in Several Variables.-
Spectral Analysis and Synthesis on Polynomial Hypergroups in a
Single Variable.- Spectral Analysis and Synthesis on Multivariate
Polynomial Hypergroups.- References.- Index.
Kyprianou, Andreas
Introductory Lectures on Fluctuations of Levy Processes with
Applications
Series: Universitext
2006, Approx. 300 p., Softcover
ISBN: 3-540-31342-7
About this textbook
Levy processes are the natural continuous-time analogue of random
walks and form a rich class of stochastic processes around which
a robust mathematical theory exists. Their mathematical
significance is justified by their application in many areas of
classical and modern stochastic models.
This text book forms the basis of a graduate course on the theory
and applications of Levy processes, from the perspective of their
path fluctuations. Central to the presentation are decompositions
of the paths of Levy processes in terms of their local maxima and
an understanding of their short- and long-term behaviour.
The book aims to be mathematically rigourous while still
providing an intuitive feel for underlying principles. The
results and applications often focus on the case of Levy
processes with jumps in only one direction, for which recent
theoretical advances have yielded a higher degree of mathematical
transparency and explicitness. Each chapter has a comprehensive
set of exercises with complete solutions.
Written for:
Graduate students in probability theory, stochastic processes,
and potential analysis
Table of contents
Levy processes and applications.- The Levy-Ito decomposition and
path structure.- More distributional and path related properties.-
Subordinators at first passage and renewal measures.- General
storage models and paths of bounded variation.- The Wiener-Hopf
factorisation.- Levy processes at first passage and insurance
risk.- Exit problems for spectrally negative processes.-
Applications to optimal stopping problems. Continuous state
branching processes and other applications.
Bushnell, Colin J., Henniart, Guy
The Local Langlands Conjecture for GL(2)
Series: Grundlehren der mathematischen Wissenschaften, Vol.
335
2006, Approx. 350 p., Hardcover
ISBN: 3-540-31486-5
About this book
If F is a non-Archimedean local field, local class field theory
can be viewed as giving a canonical bijection between the
characters of the multiplicative group GL(1,F) of F and the
characters of the Weil group of F. If n is a positive integer,
the n-dimensional analogue of a character of the multiplicative
group of F is an irreducible smooth representation of the general
linear group GL(n,F). The local Langlands Conjecture for GL(n)
postulates the existence of a canonical bijection between such
objects and n-dimensional representations of the Weil group,
generalizing class field theory.
This conjecture has now been proved for all F and n, but the
arguments are long and rely on many deep ideas and techniques.
This book gives a complete and self-contained proof of the
Langlands conjecture in the case n=2. It is aimed at graduate
students and at researchers in related fields. It presupposes no
special knowledge beyond the beginnings of the representation
theory of finite groups and the structure theory of local fields.
It uses only local methods, with no appeal to harmonic analysis
on adele groups.
Written for:
Researchers and graduate students in number theory, algebra,
geometry