A publication of the Theta Foundation.
Description
This book is dedicated to Ion Colojoara,
one of the main
contributors to the development of spectral
theory in Banach
spaces. It contains survey papers and a careful
selection of
research papers by Colojoara's colleagues,
former students, and
prominent researchers in the field.
Topics include:
growth properties of resolvents
positive definite operator measures and operator-valued
functions
spectral spaces of bounded operators
realization techniques for analytic functions
of several
variables
perturbation theory and spectral resolutions
in Krein spaces
orthogonal polynomials in several non-commuting
variables
idempotent linear relations and generalized
projection on Hilbert
spaces
The book is suitable for graduate students
and researchers
interested in operator theory.
Contents
E. Albrecht and W. Ricker -- Local spectral
theory for operators
with thin spectrum
C.-G. Ambrozie -- A remark on operator-valued
positive-definite
functions
T. Ya. Azizov and V. A. Straus -- Spectral
decompositions for
special classes of self-adjoint and normal
operators on Krein
spaces
T. Constantinescu -- Orthogonal polynomials
in several non-commuting
variables. I.
J. Eschmeier and M. Putinar -- On bounded
analytic extensions in
$\mathbb{C}^n$
P. Jonas -- On locally definite operators
in Krein spaces
J.-P. Labrousse -- Idempotent linear relations
V. Lyance and G. Chuiko -- Rings of projectors
and operator-valued
measures
M. Sabac -- Commutators, intertwining operators
and invariant
subspaces
F.-H. Vasilescu -- Spectral measures and
moment problems
Details:
Publisher: Theta Foundation
ISBN: 973-85432-3-1
Paging: 216 pp.
Binding: Hardcover
Description
This book contains the latest developments
in a central theme of
research on analysis of one complex variable.
The material is
based on lectures at the University of Michigan.
The exposition is about understanding the
geometry of
interpolating and sampling sequences in classical
spaces of
analytic functions. The subject can be viewed
as arising from
three classical topics: Nevanlinna-Pick interpolation,
Carleson's
interpolation theorem for H^infty, and the
sampling theorem, also
known as the Whittaker-Kotelnikov-Shannon
theorem.
The author clarifies how certain basic properties
of the space at
hand are reflected in the geometry of interpolating
and sampling
sequences. Key words for the geometric descriptions
are Carleson
measures, Beurling densities, the Nyquist
rate, and the Helson-Szego
condition.
Seip writes in a relaxed and fairly informal
style, successfully
blending informal explanations with technical
details. The result
is a very readable account of this complex
topic.
Prerequisites are a basic knowledge of complex
and functional
analysis. Beyond that, readers should have
some familiarity with
the basics of H^p theory and BMO.
Contents
Carleson's interpolation theorem
Interpolating sequences and the Pick property
Interpolation and sampling in Bergman spaces
Interpolation in the Bloch space
Interpolation, sampling, and Toeplitz operators
Interpolation and sampling in Paley-Wiener
spaces
Bibliography
Index
Details:
Series: University Lecture Series,Volume:
33
Publication Year: 2004
ISBN: 0-8218-3554-8
Paging: 139 pp.
Binding: Softcover
(Pure and Applied Mathematics, Volume 141)
Serves as both an introduction to the field
and as a reference
book.
Contains numerous exercises desgined to aid
students and readers.
Self-contained chapters provide helpful guidance
for lectures.
Infinite Words is an important theory in
both Mathematics and
Computer Sciences. Many new developments
have been made in the
field, encouraged by its application to problems
in computer
science. Infinite Words is the first manual
devoted to this topic.
Infinite Words explores all aspects of the
theory, including
Automata, Semigroups, Topology, Games, Logic,
Bi-infinite Words,
Infinite Trees and Finite Words. The book
also looks at the early
pioneering work of Buchi, McNaughton and
Schutzenberger.
ISBN: 0-12-532111-2 Book/Hardback
Measurements: 6 X 9 in
Pages: 450
Imprint: Academic Press
Publication Date: 18 February 2004
Publication is planned for July 2004 | Paperback
| 300 pages |
ISBN: 0-521-60305-6
Within algebraic topology, the prominent
role of multiplicative
cohomology theories has led to a great deal
of foundational
research on ring spectra and in the 1990's
this gave rise to
significant new approaches to constructing
categories of spectra
and ring-like objects in them. This book
contains some important
new contributions to the theory of structured
ring spectra as
well as survey papers describing these and
relationships between
them. One important aspect is the study of
strict multiplicative
structures on spectra and the development
of obstruction theories
to imposing strictly associative and commutative
ring structures
on spectra. A different topic is the transfer
of classical
algebraic methods and ideas, such as Morita
theory, to the world
of stable homotopy.
Contributors
Andrew Baker, Birgit Richter, Andrey Lazarev,
Stefan Schwede,
Michael Joachim, Anthony Elmendorf, Michael
Mandell, Paul Goerss,
Michael Hopkins, Alan Robinson, Maria Basterra
Contents
1. The development of structured ring spectra
Anthony Elmendorf;
2. Compromises forced by Lewis’s Theorem
Anthony Elmendorf; 3.
Permutative categories as a model of connective
stable homotopy
Anthony Elmendorf and Michael Mandell; 4.
Morita Theory in
Abelian, derived and stable model categories
Stefan Schwede; 5.
Higher coherences in equivariant K-theory
Michael Joachim; 6. Co-Homology
theories for commutative S-Algebras Maria
Basterra and Birgit
Richter; 7. Classical obstructions and S-Algebras
Alan Robinson;
8. Moduli spaces of commutative ring spectra
Paul Goerss and
Michael Hopkins; 9. Cohomology theories for
highly structured
ring spectra Andrey Lazarev.
Publication is planned for August 2004 |
Hardback | 150 pages
20 figures | ISBN: 0-521-83805-3
Information retrieval, IR, the science of
extracting information
from any potential source, can be viewed
in a number of ways:
logical, probabilistic and vector space models
are some of the
most important. In this book, the author,
one of the leading
researchers in the area, shows how these
views can be reforged in
the same framework used to formulate the
general principles of
quantum mechanics. All the usual quantum-mechanical
notions have
their IR-theoretic analogues, and the standard
results can be
applied to address problems in IR, such as
pseudo-relevance
feedback, relevance feedback and ostensive
retrieval. The
relation with quantum computing is also examined.
To keep the
book self-contained appendices with background
material on
physics and mathematics are included. Each
chapter ends with
bibliographic remarks that point to further
reading. This is an
important, ground-breaking book, with much
new material, for all
those working in IR, AI and natural language
processing.
Contents
Preface; Prologue; 1. Introduction; 2. On
sets and kinds in IR; 3.
Vector and Hilbert spaces; 4. Linear transformations,
operators
and matrices; 5. Conditional logic in IR;
6. The geometry of IR;
Appendix I. Linear algebra; Appendix II.
Quantum mechanics;
Appendix III. Probability; Bibliography;
Index.