Xiao, J., Concordia University, Montreal, QC, Canada
Holomorphic Q Classes
2001. VIII, 112 pp. Softcover
3-540-42625-6
The space Q p consists of all holomorphic
functions f on the unit
disk for which the L^2 area integrals of
its derivative against
the p-th power of the Green function of the
unit disk are
uniformly bounded in the variable that survives
the integration.
It turns out that Q 1 coincides with BMOA,
while, for p>1, Q p
are just the Bloch space. For p/in (0,1)
the Q p furnish an
increasing sequence of spaces, each invariant
under conformal
mappings of the unit disk onto itself, which
interpolate between
the Dirichlet space and BMOA. This monograph
covers a number of
important aspects in complex, functional
and harmonic analysis.
The primary focus is Q p, p/in (0,1), and
their equivalent
characterizations. Based on the up-to-date
results obtained by
experts in their respective fields, each
of the eight chapters
unfolds from the basics to the more complex.
The exposition here
is rapid-paced and efficient, with proofs
and examples.
Keywords: $ Q p $, BMOA, Bloch Space, Characterization,
Conformally Invariant StructureMSC ( 2000
): 30D545, 30H05, 31A20,
32A37, 41A15, 46E15, 46G10, 47B33, 47B38
Contents: 1. Fundamental Material
1.1 Introduction
1.2 Inclusion
1.3 Image Area
Notes
2. Composite Embedding
2.1 Existence of BiBloch-Type Mappings
2.2 Boundedness and Compactness
2.3 Geometric Characterizations
Notes
3. Series Expansion
3.1 Power Series
3.2 Partial Sums
3.3 Nonnegative Coefficients
3.4 Random Series
Notes
4. Modified Carleson Measures
4.1 An Integral Form
4.2 Relating to Mean Lipschitz Spaces
4.3 Comparison with Besov Spaces
4.4 Mean Growth
Notes
5. Inner-Outer Structure
5.1 Singular Facturs
5.2 Blaschke Products
5.3 Outer Functions
5.4 Canonical Factorization
Notes
6. Pseudo-holomorphic Extension
6.1 Boundary Value Behavior
6.2 Weight Condition
6.3 Pseudo-holomorphic Continuation
6.4 K-property
Notes
7. Representation via /bar/partial-equation
7.1 Harmonic Extension
7.2 /bar/partial-estimates
7.3 Fefferman-Stein Type Decomposition
7.4 Corona Data and Solutions
7.5 Interpolating Sequences
Notes
8. Dyadic Localization
8.1 Square Mean Oscillation
8.2 Dyadic Model
8.3 Wavelets
Notes
References
Index
Series: Lecture Notes in Mathematics. VOL.
1767
Anile, M., University of Catania, Italy Capasso,
V., University of Milano, Italy Greco, A.,
University of Palermo, Italy (Eds.)
Progress in Industrial Mathematics at ECMI
2000
2002. XIV, 713 pp. Hardcover
3-540-42582-9
The European Consortium for Mathematics in
Industry (ECMI) was
founded in 1986 by leading groups of mathematicians
in Europe for
the following scopes:
i) direct involvement of mathematicians in
R&D activities;
ii) international cooperation at a European
scale;
iii) education of industrial mathematicians
to meet the growing
demand for such experts.
ECMI 2000 shows that ECMI has offered a unique
example of
effective international cooperation thanks
to the financial
support of the European Framework programmes.
In particular they
have helped ECMI establishing a set of Special
Interest Groups to
favour interaction with industry. This volume
includes
minisymposia about their activities, in particular
microelectronics, glass, polymers, finance,
traffic, and textiles.
Applied mathematicians and other professionals
working in
academia or industry will find the book to
be a useful and
stimulating source of mathematical applications
related to
industrial problems.
Keywords: Mathematics in Industry, Mathematics
in Finance,
Computational Science and Engineering, Optimization,
Mathematics
in Medicine
Contents: Plenary talks.- Minisymposia: Finance;
Fuel pipelines;
Image processing: linear and nonlinear techniques;
Information
and communication technologies; Kinetic transport
in
semiconductor devices; Liquid/solid phase
transictions and
interfaces; Mathematical problems in glass
industry;
Microelectronics; Models of highway traffic;
Models from the
texile industry; Numerical methods for hyperbolic
and kinetic
equations; Problems of charge transport in
semiconductor
nanostructures; Polymers; Some applications
of fluid and gas
dynamics; Teaching of industrial mathematics
at ECMI centers.-
Contributed talks.
Series: Mathematics in Industry. VOL. 1
Anishchenko, V.S., Saratov State University, Saratov,
Russia Astakhov, V., Saratov State University,
Saratov, Russia Neiman, A., Saratov State
University, Saratov, Russia Vadivasova, T.,
Saratov State University, Saratov, Russia
Schimansky-Geier, L., Humboldt-Universitat
zu Berlin, Germany
Nonlinear Dynamics of Chaotic and Stochastic
Systems
Tutorial and Modern Developments
2001. XIII, 372 pp. 173 figs. Hardcover
3-540-42419-9
This book is a complete treatise on the theory
of nonlinear
dynamics of chaotic and stochastic systems.
It contains both an
exhaustive introduction to the subject as
well as a detailed
discussion of fundamental problems and research
results in a
field to which the authors have made important
contributions
themselves. Despite the unified presentation
of the subject, care
has been taken to present the material in
largely self-contained
chapters.
The present book can thus be used either
as a textbook by
graduate students or as a modern monograph
by researchers in this
field.
Keywords: Nonlinear Dynamics Chaos Stochastic
Systems Dynamical
Systems
Contents: From the contents: Tutorial.- Dynamical
Systems.-
Fluctuations in Dynamic Systems.- Synchronization
of Periodic
Systems.- Dynamical Chaos.- Routes to Chaos.-
Synchronization of
Chaos.- Controlling Chaos.- Reconstruction
of Dynamical Systems.-
Stochastic Dynamics.- Stochastic Resonance.-
Synchronization of
Stochastic Systems.- The Beneficial Role
of Noise in Excitable
Systems.- Noise Induced Transport.
Series: Springer Series in Synergetics.
Cyganowski, S., Tipperary, Ireland Kloeden, P., Johann-Wolgang-Goethe
Universitat, Frankfurt/Main, Germany Ombach,
J., Jagiellonian University, Krakow, Poland
From Elementary Probability to Stochastic
Differential Equations with MAPLE
2002. XVI, 313 pp. Softcover
3-540-42666-3
The authors provide a fast introduction to
probabilistic and
statistical concepts necessary to understand
the basic ideas and
methods of stochastic differential equations.
The book is based
on measure theory which is introduced as
smoothly as possible. It
is intended for advanced undergraduate students
or graduates, not
necessarily in mathematics, providing an
overview and intuitive
background for more advanced studies as well
as some practical
skills in the use of MAPLE in the context
of probability and its
applications. As prerequisites the authors
assume a familiarity
with basic calculus and linear algebra, as
well as with
elementary ordinary differential equations
and, in the final
chapter, simple numerical methods for such
ODEs. Although
statistics is not systematically treated,
they introduce
statistical concepts such as sampling, estimators,
hypothesis
testing, confidence intervals, significance
levels and p-values
and use them in a large number of examples,
problems and
simulations.
Keywords: probability, stochastic differential
equations,
statistics, symbolic computation
Series: Universitext.
Arveson, W., University of California at Berkeley,
CA, USA
A Short Course on Spectral Theory
2001. Approx. 150 pp. Hardcover
0-387-95300-0
This book presents the basic tools of modern
analysis within the
context of the fundamental problem of operator
theory: to
calculate spectra of specific operators on
infinite dimensional
spaces, especially operators on Hilbert spaces.
The tools are
diverse, and they provide the basis for more
refined methods that
allow one to approach problems that go well
beyond the
computation of spectra: the mathematical
foundations of quantum
physics, noncommutative k-theory, and the
classification of
simple C*-algebras being three areas of current
research activity
which require mastery of the material presented
here. The book is
based on a fifteen-week course which the
author offered to first
or second year graduate students with a foundation
in measure
theory and elementary functional analysis.
Keywords: Spectral Theory, Banach Algebra,
C * Algebra
Contents: Spectral theory and Banach algebras.-
Operators on
Hilbert space.- Asymptotics: compact perturbations
and Fredholm
theory.- Methods and applications.- Bibliography.-
Index.
Series: Graduate Texts in Mathematics. VOL.
209