2003 XIV, 154 p. 10 illus. Softcover
3-7643-3242-5
This self-contained work on Hilbert space
operators takes a
problem-solving approach to the subject,
combining theoretical
results with a wide variety of exercises
that range from the
straightforward to the state of the art.
Complete solutions to
all problems are provided. The text covers
the basics of bounded
linear operators on a Hilbert space and gradually
progresses to
more advanced topics in spectral theory and
quasireducible
operators.
Written in a motivating and rigorous style,
the work has few
prerequisites beyond elementary functional
analysis, and will
appeal to graduate students and researchers
in mathematics,
physics, engineering, and related disciplines.
Contents:
Preface * Invariant Subspaces * Hilbert Space
Operators *
Convergence and Stability * Reducing Subspaces
* Shifts *
Decompositions * Orthogonality * Hyponormal
Operators * Spectral
Properties * Paranormal Operators * Proper
Contractions *
Quasireducible Operators * The Lomonosov
Theorem * Bibliography *
Index
2004 Approx. 448 p., 92 illus. Hardcover
3-7643-4279-X
Transforms have diverse applications in digital
signal processing
and other areas of science, engineering,
and technology. Indeed,
new transforms are continuously emerging
to solve many new or
open problems created by technological advances.
To improve the
implementation of these transforms, fast
algorithms have been
created and widely used over the last forty
years. Although
closely related to the discrete Fourier transform,
novel fast
algorithms for various transforms have to
be developed separately
in order to minimize computational complexity
and implementation
costs.
This book is a comprehensive presentation
of results and recent
progress on several commonly used transforms
and their fast
algorithms. In many cases, additional options
are provided for
new or improved fast algorithms, some not
yet well known in the
digital signal processing community. Demonstrated
throughout the
work is the potential for fast algorithms
to meet the demands
created by fast computing processors, which
may lead to advances
in modern applications.
The work is suitable as a textbook for senior
undergraduate and
graduate students; it may also be used as
a self-study reference
for electrical engineers and applied mathematicians
working in
the fields of electronics, signal, image
and speech processing,
or digital design and communication.
Keywords: Algorithms, Harmonic Analysis,
Signal Processing
Contents:
Introduction * Polynomial Transforms and
Their Fast Algorithms *
Fast Fourier Transform Algorithms * Fast
Algorithms for 1D
Discrete Hartley Transforms * Fast Algorithms
for MD Discrete
Hartley Transforms * Fast Algorithms for
1D Discrete Cosine
Transforms * Fast Algorithms for MD Discrete
Cosine Transform *
Integer Transforms and Fast Algorithms *
New Methods of Time-Frequency
Analysis * Index
Series: ANHA* Applied and Numerical Harmonic
Analysis.
2003 X, 454 p. Hardcover
3-7643-2189-X
Assuming that the reader is familiar with
sheaf theory, the book
gives a self-contained introduction to the
theory of
constructible sheaves related to many kinds
of singular spaces,
such as cell complexes, triangulated spaces,
semialgebraic and
subanalytic sets, complex algebraic or analytic
sets, stratified
spaces, and quotient spaces. The relation
to the underlying
geometrical ideas are worked out in detail,
together with many
applications to the topology of such spaces.
All chapters have
their own detailed introduction, containing
the main results and
definitions, illustrated in simple terms
by a number of examples.
The technical details of the proof are postponed
to later
sections, since these are not needed for
the applications.
Keywords: Algabraic topology, Sheaves, Singular
spaces,
Monodromy, Algebraic geometry, Category theory,
Triangulation,
Localization, Morse theory
Contents:
Introduction.- 1. Thom-Sebastiani Theorem
for Constructible
Sheaves.- 2. Constructible Sheaves in Geometric
Categories.- 3.
Localization Results for Equivariant Constructible
Sheaves.- 4.
Stratification Theory and Constructible Sheaves.-
5. Morse Theory
for Constructible Sheaves.- 6. Vanishing
Theorems for
Constructible Sheaves.- Bibliography.- Index.
Series: Monografie Matematyczne. Vol.. 63
2003 Approx. 350 p. Hardcover
3-7643-4304-4
Sampling, wavelets, and tomography are three
active areas of
contemporary mathematics sharing common roots
that lie at the
heart of harmonic and Fourier analysis. The
advent of new
techniques in mathematical analysis has strengthened
their
interdependence and led to some new and interesting
results in
the field.
This state-of-the-art book not only presents
new results in these
research areas, but it also demonstrates
the role of sampling in
both wavelet theory and tomography. Specific
topics covered
include:
* Robustness of Regular Sampling in Sobolev
Algebras * Irregular
and Semi-Irregular Weyl-Heisenberg Frames
* Adaptive Irregular
Sampling in Meshfree Flow Simulation * Sampling
Theorems for Non-Bandlimited
Signals * Polynomial Matrix Factorization,
Multidimensional
Filter Banks, and Wavelets * Generalized
Frame Multiresolution
Analysis of Abstract Hilbert Spaces * Sampling
Theory and
Parallel-Beam Tomography * Thin-Plate Spline
Interpolation in
Medical Imaging * Filtered Back-Projection
Algorithms for Spiral
Cone Computed Tomography
Aimed at mathematicians, scientists, and
engineers working in
signal and image processing and medical imaging,
the work is
designed to be accessible to an audience
with diverse
mathematical backgrounds. Although the volume
reflects the
contributions of renowned mathematicians
and engineers, each
chapter has an expository introduction written
for the non-specialist.
One of the key features of the book is an
introductory chapter
stressing the interdependence of the three
main areas covered. A
comprehensive index completes the work.
Contributors: J.J. Benedetto, N.K. Bose,
P.G. Casazza, Y.C.
Eldar, H.G. Feichtinger, A. Faridani, A.
Iske, S. Jaffard, A.
Katsevich, S. Lertrattanapanich, G. Lauritsch,
B. Mair, M.
Papadakis, P.P. Vaidyanathan, T. Werther,
D.C. Wilson, A.I. Zayed
Contents:
A Prelude to Sampling, Wavelets, and Tomography
(Ahmed I. Zayed)
* Part I: Sampling and Frames * Sampling
Without Input
Constraints: Consistent Reconstruction in
Arbitrary Spaces (Yonina
C. Eldar) * An Introduction to Irregular
Weyl-Heisenberg Frames (Peter
G. Casazza) * Robustness of Regular Sampling
in Sobolev Algebras
(Hans G. Feichtinger and Tobias Werther)
* Adaptive Irregular
Sampling in Meshfree Flow Simulation (Armin
Iske) * Part II:
Wavelets * Polynomial Matrix Factorization,
Multidimensional
Filter Banks and Wavelets (N. K. Bose and
S. Lertrattanapanich) *
Sampling Theorems for Non-Bandlimited Signals
(P. P. Vaidyanathan)
* Function Spaces Based on Wavelet Expansions
(Stephane Jaffard)
* Generalized Frame Multiresolution Analysis
of Abstract Hilbert
Spaces (Manos Papadakis) * Part III: Tomography
* Sampling Theory
and Parallel-Beam Tomography (Adel Faridani)
* Filtered
Backprojection Algorithms For Spiral Cone
Beam CT (Alexander
Katsevich and Guenter Lauritsch) * Thin-Plate
Spline
Interpolation (David C. Wilson and Bernard
Mair) * Index
Series: ANHA: Applied and Numerical Harmonic
Analysis.
1st ed. 2002. Corr. 2nd printing 2003 Approx.
340 p. Softcover
3-7643-2171-7
Pattern formation in physical systems is
one of the major
research frontiers of mathematics. A central
theme of this book
is that many instances of pattern formation
can be understood
within a single framework: symmetry.
The book applies symmetry methods to increasingly
complex kinds
of dynamic behavior: equilibria, period-doubling,
time-periodic
states, homoclinic and heteroclinic orbits,
and chaos. Examples
are drawn from both ODEs and PDEs. In each
case the type of
dynamical behavior being studied is motivated
through
applications, drawn from a wide variety of
scientific disciplines
ranging from theoretical physics to evolutionary
biology. An
extensive bibliography is provided.
Keywords: Chaos, Fractals, Dynamical Systems
Contents:
Preface.- Steady-State Bifurcation.- Linear
Stability.- Time
Periodicity and Spatio-Temporal Symmetry.-
Hopf Bifurcation with
Symmetry.- Steady-State Bifurcations in Euclidean
Equivariant
Systems.- Bifurcation From Group Orbits.-
Hidden Symmetry and
Genericity.- Heteroclinic Cycles.- Symmetric
Chaos.- Periodic
Solutions of Symmetric Hamiltonian Systems.