Progress in Nonlinear Differential Equations,
Vol.50
2002. Approx. 500 pages. Hardcover
ISBN 3-7643-6791-1
English
Due in July 2002
Brunello Terreni (1953-2000) was a researcher
and teacher with
vision and dedication.
The present volume is dedicated to the memory
of Brunello Terreni.
His mathematical interests are refelcted
in 20 expository
articles written by distinguished mathematicians.
The unifying
theme of the articles is evolution equations
and functional
analysis, which is presented in various and
diverse forms:
parabolic equations, semigroups, stochastic
evolution, optimal
control, existence, uniqueness and regularity
of solutions,
inverse problems as well as applications.
Contributors: P. Acquistapace, V. Barbu,
A. Briani, L. Boccardo,
P. Colli Franzone, G. Da Prato, D. Donatelli,
A. Favini, M.
Fuhrmann, M. Grasselli, R. Illner, H. Koch,
R. Labbas, H. Lange,
I. Lasiecka, A. Lorenzi, A. Lunardi, P. Marcati,
R. Nagel, G.
Nickel, V. Pata, M. M. Porzio, B. Ruf, G.
Savare, R. Schnaubelt,
E. Sinestrari, H. Tanabe, H. Teismann, E.
Terraneo, R. Triggiani,
A. Yagi
2002. Approx. 250 pages.
English
Due in August 2002
Hardcover
ISBN 3-7643-6905-1
Softcover
ISBN 3-7643-6792-X
Linear Algebra is one of the most important
branches of
mathematics - important because of its many
applications to other
areas of mathematics, and important because
it contains a wealth
of ideas and results which are basic to pure
mathematics.
This book gives an introduction to linear
algebra, and develops
and proves its fundamental properties and
theorems taking a pure
mathematical approach - linear algebra contains
some fine pure
mathematics.
Main topics:
vector spaces and algebras, dimension, linear
maps, direct sums,
and (briefly) exact sequences
matrices and their connections with linear
maps, determinants (properties
proved using some elementary group theory),
and linear equations
Cayley-Hamilton and Jordan theorems leading
to the spectrum of a
linear map - this provides a geometric-type
description of these
maps
Hermitian and inner product spaces introducing
some metric
properties (distance, perpendicularity etc.)
into the theory,
also unitary and orthogonal maps and matrices
applications to finite fields, mathematical
coding theory, finite
matrix groups, the geometry of quadratic
forms, quaternions and
Cayley numbers, and some basic group representation
theory
A large number of examples, exercises and
problems are provided.
Answers and/or sketch solutions to all of
the problems are given
in an appendix. Some of these are theoretical
and some numerical,
both types are important. No particular computer
algebra package
is discussed but a number of the exercises
are intended to be
solved using one of these packages chosen
by the reader.
The approach is pure-mathematical, and the
intended readership is
undergraduate mathematicians, also anyone
who requires a more
than basic understanding of the subject.
This book will be most
useful for a "second course" in
linar algebra, that is
for students that have seen some elementary
matrix algebra. But
as all terms are defined from scratch, the
book can be used for a
"first course" for more advanced
students.
Operator Theory: Advances and Applications,
Vol. 134
2002. 428 pages. Hardcover
ISBN 3-7643-6762-8
English
This volume is dedicated to Harry Dym, a
leading expert in
operator theory, on the occasion of his 60th
birthday.
It opens with an autobiographical sketch,
a list of publications
and a personal account of I. Gohberg on his
collaboration with
Harry Dym. The mathematical papers cover
Krein space operator
theory, Schur analysis and interpolation,
several complex
variables and Riemann surfaces, matrix theory,
system theory, and
differential equations and mathematical physics.
The book is of
interest to a wide audience of pure and applied
mathematicians,
electrical engineers and theoretical physicists.
Operator Theory: Advances and Applications,
vol.135
2002. Approx. 330 pages. Hardcover
ISBN 3-7643-6877-2
English
Due in August 2002
This volume, dedicated to Bernd Silbermann
on his sixtieth
birthday, collects research articles on Toeplitz
matrices and
singular integral equations written by leading
area experts.
The subjects of the contributions include
Banach algebraic
methods, Toeplitz determinants and random
matrix theory, Fredholm
theory and numerical analysis for singular
integral equations,
and efficient algorithms for linear systems
with structured
matrices, and reflect Bernd Silbermann's
broad spectrum of
research interests. The volume also contains
a biographical essay
and a list of publications.
The book is addressed to a wide audience
in the mathematical and
engineering sciences. The articles are carefully
written and are
accessible to motivated readers with basic
knowledge in
functional analysis and operator theory.
Progress in Mathematics
2002. Approx. 280 pages. Hardcover
ISBN 3-7643-6909-4
English
Due in September 2002
Main subject of this monograph is the study of automorphic
distributions, and of the operators associated with such
distributions under the Weyl rule of symbolic calculus. The
concept of quantization pervades the whole book: an entirely new
approach to composition formulas, in general, is needed, and the
main lines of some new program in this direction are indicated.
From the Table of Contents:
Chapter 1: Weyl Calculus, the upper Half-plane, and Automorphic
Distributions - Eisenstein Distributions, Dirac's Comb and
Bezout's Distribution - The Structure of Automorphic
Distributions
Chapter 2: A Tamer Version of the Weyl Calculus - The Higher-level
Metaplectic Representations - The Radial Parts of Relativistic
Wave Operators - The Higher-level Weyl Calculi - The Sharp-product
of two Power-Functions: the Weyl Case - Beyond the Symplectic
Group
Chapter 3: The Sharp Composition of Automorphic Distributions -
The Roelcke-Selberg Expansion
Chapter 4: Further Perspectives - Another Way to Compose Weyl
Symbols - Odd Automorphic Distributions and Modular Forms of Non-zero
Weight - New Perspectives and Problems in Quantization Theory