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This volume is the first of the three volume publication containing
the proceedings of the 1989 International Symposium on the
Mathematical Theory of Networks and Systems (MTNS-89), which was
held in Amsterdam, The Netherlands, June 19-23, 1989. The
International Symposia MTNS focus attention on problems from system
and control theory, circuit theory and signal processing, which, in
general, require application of sophisticated mathematical tools,
such as from function and operator theory, linear algebra and
matrix theory, differential and algebraic geometry. The interaction
between advanced mathematical methods and practical engineering
problems of circuits, systems and control, which is typical for
MTNS, turns out to be most effective and is, as these proceedings
show, a continuing source of exciting advances. The first volume
contains invited papers and a large selection of other symposium
presentations on the general theory of deterministic and stochastic
systems with an emphasis on realization and modelling. A wide
variety of recent results on approximate realization and system
identification, stochastic dynamical systems, discrete event
systems, - o systems, singular systems and nonstandard models IS
presented. Preface vi Also a few papers on applications in
hydrology and hydraulics are included. The titles of the two other
volumes are: Robust Control of Linear Sys tems and Nonlinear
Control (volume 2) and Signal Processing. Scatter ing and Operator
Theory. and Numerical Methods (volume 3). The Editors are most
grateful to the about 300 reviewers for their help in the
refereeing process. The Editors thank Ms. G. Bijleveld and Ms."
This book is devoted to a new direction in linear algebra and
operator theory that deals with the invariants of partially
specified matrices and operators, and with the spectral analysis of
their completions. The theory developed centers around two major
problems concerning matrices of which part of the entries are given
and the others are unspecified. The first is a classification
problem and aims at a simplification of the given part with the
help of admissible similarities. The results here may be seen as a
far reaching generalization of the Jordan canonical form. The
second problem is called the eigenvalue completion problem and asks
to describe all possible eigenvalues and their multiplicities of
the matrices which one obtains by filling in the unspecified
entries. Both problems are also considered in an infinite
dimensional operator framework. A large part of the book deals with
applications to matrix theory and analysis, namely to stabilization
problems in mathematical system theory, to problems of Wiener-Hopf
factorization and interpolation for matrix polynomials and rational
matrix functions, to the Kronecker structure theory of linear
pencils, and to non everywhere defined operators. The eigenvalue
completion problem has a natural associated inverse, which appears
as a restriction problem. The analysis of these two problems is
often simpler when a solution of the corresponding classification
problem is available."
A comprehensive graduate textbook that introduces functional
analysis with an emphasis on the theory of linear operators and its
application to differential equations, integral equations, infinite
systems of linear equations, approximation theory, and numerical
analysis. As a textbook designed for senior undergraduate and
graduate students, it begins with the geometry of Hilbert spaces
and proceeds to the theory of linear operators on these spaces
including Banach spaces. Presented as a natural continuation of
linear algebra, the book provides a firm foundation in operator
theory which is an essential part of mathematical training for
students of mathematics, engineering, and other technical sciences.
After the book "Basic Operator Theory" by Gohberg-Goldberg was pub
lished, we, that is the present authors, intended to continue with
another book which would show the readers the large variety of
classes of operators and the important role they play in
applications. The book was planned to be of modest size, but due to
the profusion of results in this area of analysis, the number of
topics grew larger than ex pected. Consequently, we decided to
divide the material into two volumes - the first volume being
presented now. During the past years, courses and seminars were
given at our respective in stitutions based on parts of the texts.
These were well received by the audience and enabled us to make
appropriate choices for the topics and presentation for the two vol
umes. We would like to thank G.J. Groenewald, A.B. Kuijper and
A.C.M. Ran of the Vrije Universiteit at Amsterdam, who provided us
with lists of remarks and corrections. We are now aware that the
Basic Operator Theory book should be revised so that it may
suitably fit in with our present volumes. This revision is planned
to be the last step of an induction and not the first."
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