Alpay, Daniel; Gohberg, Israel (Eds.)
Interpolation, Schur Functions and Moment Problems
Series: Operator Theory: Advances and Applications
Subseries: Linear Operators and Linear Systems, Vol. 165
2006, Approx. 315 p., Hardcover
ISBN: 3-7643-7546-9
About this book
Schur analysis originates with a 1917 paper by Schur where he
associated to a function analytic and contractive in the open
unit disk a sequence, finite or infinite, of numbers in
the open unit disk, called Schur coefficients. In signal
processing, they are often called reflection coefficients. Under
the word "Schur analysis" one encounters a variety of
problems related to Schur functions such as interpolation
problems, moment problems, study of the relationships between the
Schur coefficients and the properties of the function, study of
underlying operators and others.
This volume is almost entirely dedicated to the analysis of Schur
and Caratheodory functions and to the solutions of problems for
these classes.
Written for:
Postgraduates and researchers in operator and systems theory
Table of contents
Editorial introduction.- Basic Boundary Interpolation for
Generalized Schur Functions and Factorization of Rational J-Unitary
Matrix Functions.- Discrete Analogs of Canonical Systems with
Pseudo-exponential Potential. Inverse Problems.- Boundary
Nevanlinna-Pick Interpolation Problems for Generalized Schur
Functions.- A Truncated Matricial Moment Problem on a Finite
Interval.- Shift Operators Contained in Contractions, Schur
Parameters and Pseudo-continuable Schur Functions.- The Matricial
Caratheodory Problem in Both Nondegenerate and Degenerate Cases.-
A Gohberg-Heinig Type Inversion Formula Involving Hankel
Operators.
Clark, J., Lomp, C., Vanaja, N., Wisbauer, R.
Lifting Modules
Series: Frontiers in Mathematics
2006, Approx. 400 p., Softcover
ISBN: 3-7643-7572-8
A Birkhauser book
About this book
Extending modules are generalizations of injective modules and,
dually, lifting modules generalize projective supplemented
modules. There is a certain asymmetry in this duality. While the
theory of extending modules is well documented in monographs and
text books, the purpose of our monograph is to provide a thorough
study of supplements and projectivity conditions needed to
investigate classes of modules related to lifting modules.
Written for:
Graduate students and researchers in algebra
Table of contents
Preface.- Notation.- 1. Basic Notions.- 2. Preradicals and
Torsion Theories.- 3. Decompositions of Modules.- 4. Supplements
in Modules.- 5. From Lifting to Perfect Modules.- 6. Special
Classes of Lifting Modules.- Appendix.- Bibliography.- Index.
Hu, Pei-Chu, Yang, Chung-Chun
Value Distribution Theory Related to Number Theory
2006, Approx. 540 p., Hardcover
ISBN: 3-7643-7568-X
About this book
The subject of the book is Diophantine approximation and
Nevanlinna theory (number theory, complex analysis).
For example, heights in number theory with characteristic
functions in Nevanlinna theory are compared; Roth's theorem with
Nevanlinna's second main theorem; Schmidt subspace theorem with
Cartan's second main theorem; Bombieri-Lang conjecture with Green-Griffiths
conjecture; abc-conjecture with Mason theorem; Vojta's conjecture
with conjectures of Griffiths and Lang; and so on. The authors
also propose generalized abc-conjecture, generalized Hall's
conjecture, generalized Fermat last theorem, and prove their
analogues over complex field and non-Archimedean fields. They
discuss meromorphic solutions of Fermat equations and Waring
problem, and introduce a proof of Green-Griffiths conjecture.
Finally, they introduce some necessary and sufficient conditions
on Riemann hypothesis.
Written for:
Undergraduates and postgraduates in department of mathematics;
mathematicians in pure mathematics
Table of contents
Preface.- 1. Heights.- 2. Nevanlinna Theory.- 3. Topics in Number
Theory.- 4. Function Solutions of Diophantine Equations.- 5.
Functions over Non-Archimedean Fields.- 6. Holomorphic Curves in
Canonical Varieties.- 7. Riemann's Zeta-Function.- Bibliography.-
Index.
de Gosson, Maurice A.
Symplectic Geometry and Quantum Mechanics
Series: Operator Theory: Advances and Applications
Subseries: Advances in Partial Differential Equations, Vol. 166
2006, Approx. 400 p., Hardcover
ISBN: 3-7643-7574-4
About this book
This book is devoted to a rather complete discussion of
techniques and topics intervening in the mathematical treatment
of quantum and semi-classical mechanics. It starts with a very
readable introduction to symplectic geometry. Many topics are
also of genuine interest for pure mathematicians working in
geometry and topology.
Written for:
Mathematical physicists as well as pure and applied
mathematicians
Table of contents
Preface.- Notation.- I. Symplectic Geometry.- 1. Symplectic
Spaces and Lagrangian Planes.- 2. The Symplectic Group.- 3. Multi-Oriented
Symplectic Geometry.- 4. Intersection Indices.- II. Heisenberg
Group, Weyl Calculus, and Metaplectic Representation.- 5.
Lagrangian Manifolds and Quantization.- 6. Heisenberg Group and
Weyl Operators.- 7. The Metaplectic Group.- III. Quantum
Mechanics in Phase Space.- 8. The Uncertainty Principle.- 9. The
Density Operator.- 10. A Phase Space Weyl Calculus.- Appendices.-
Bibliography.- Index.
Alpay, Daniel (Ed.)
Wavelets, Multiscale Systems and Hypercomplex Analysis
Series: Operator Theory: Advances and Applications, Vol. 167
2006, Approx. 200 p., Hardcover
ISBN: 3-7643-7587-6
A Birkhauser book
About this book
From a mathematical point of view it is fascinating to realize
that most, if not all, of the notions arising from the theory of
analytic functions in the open unit disk have counterparts when
one replaces the integers by the nodes of a homogeneous tree. It
is also fascinating to realize that a whole function theory,
different from the classical theory of several complex variables,
can be developped when one considers hypercomplex (Clifford)
variables, Fueter polynomials and the Cauchy-Kovalevskaya
product, in place of the classical polynomials in three
independent variables.
This volume contains a selection of papers on the topics of
Clifford analysis and wavelets and multiscale analysis, the
latter being understood in a very wide sense. The theory of
wavelets is mathematically rich and has many practical
applications.
Written for:
Graduates, postgraduates and researchers; engineers
Table of contents
Editorial Introduction.- Teodorescu Transform Decomposition of
Multivector Fields on Fractal Hypersurfaces.- Metric Dependent
Clifford Analysis with Applications to Wavelet Analysis.- A
Hierarchical Semi-Separable Moore-Penrose Equation Solver.-
Methods from Multiscale Theory and Wavelets Applied to Nonlinear
Dynamics.- Noncommutative Trigonometry.- Stationary Random Fields
over Graphs.- Matrix Representations and Numerical Computations
of Wavelet Multipliers.- Clifford algebra-valued Admissible
Wavelets.
Andreescu, Titu, Andrica, Dorin
Number Theory
A Problem-Solving Approach
2006, Approx. 300 p. 150 illus., Hardcover
ISBN: 0-8176-3245-X
About this textbook
One of the oldest, liveliest branches of mathematics, number
theory is noted for its theoretical depth and applications to
other fields, including representation theory, physics, and
cryptography. The forefront of number theory is replete with
sophisticated and famous open problems; at its foundation,
however, are basic, elementary ideas that can stimulate and
challenge beginning students.
This introductory textbook takes a problem-solving approach to
number theory, situating each concept within the framework of an
example or a problem for readers to solve. Starting with the
essentials, the text covers divisibility, unique factorization,
modular arithmetic and the Chinese Remainder Theorem, Diophantine
equations, binomial coefficients, Fermat and Mersenne primes and
other special numbers, special sequences, and problems of density.
Included are sections on mathematical induction and the
pigeonhole principle, as well as a discussion of other number
systems.
By emphasizing examples and applications, and by introducing and
reinforcing every idea with an exercise, the authors motivate and
engage readers. The exposition proceeds incrementally from first
principles, starting with the natural numbers and then
intuitively and rigorously uncovering deeper properties. A
comprehensive index and selected solutions complete the work.
Written by distinguished research mathematicians and renowned
teachers, "Number Theory: A Problem-Solving Approach"
will appeal to senior high school and undergraduate students and
instructors. It is a clear, accessible introduction to the
subject and a source of fascinating problems and puzzles for
readers at all levels.
Written for:
Undergraduates, advanced high school students, instructors,
general audience
Table of contents
The Natural Numbers: An Introduction .- Prime Numbers,
Divisibility and the Euclidean Algorithm .- Parity and Modular
Systems .- Linear Diophantine Equations .- Some Classic Results:
Fermat, Euler, and Wilson .- Quadratic Residues .- Quadratic
Diophantine Equations .- Some More Advanced Topics.