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This little collection of poems, stories, outbursts and musings is
put forward as an homage to Jerome K. Jerome. His book, Idle
Thoughts of an Idle Fellow, published in 1886, is like mine, a
series of humorous articles on various subjects.
Have you ever experienced a strong compulsion to head for the
hills? In your dreams have you ever pictured yourself running free
over some beautiful moorland landscape, with the wind in your hair
and the heather tickling you elsewhere? Perhaps, until now, you
have put it down to eating cheese before going to bed? Well, maybe
it is the Call of the North - inviting you to explore the Pennines.
Maybe it is time to set aside life's problems, step into the
footprints of the heroes of old and lose yourself in some exquisite
wilderness. Join Peter Lancaster as he dodges death and disaster
travelling the Pennines, with only 'Auntie' (his 1963 Rover) for
company...apart from his wife Jane, sheepdog and pint of beer. When
life is an uphill struggle, why not pause and take a look at the
view for a while?
This book is dedicated to the memory of Israel Gohberg (1928-2009)
- one of the great mathematicians of our time - who inspired
innumerable fellow mathematicians and directed many students. The
volume reflects the wide spectrum of Gohberg's mathematical
interests. It consists of more than 25 invited and peer-reviewed
original research papers written by his former students, co-authors
and friends. Included are contributions to single and multivariable
operator theory, commutative and non-commutative Banach algebra
theory, the theory of matrix polynomials and analytic vector-valued
functions, several variable complex function theory, and the theory
of structured matrices and operators. Also treated are canonical
differential systems, interpolation, completion and extension
problems, numerical linear algebra and mathematical systems theory.
In this article we shall use two special classes of reproducing
kernel Hilbert spaces (which originate in the work of de Branges
[dB) and de Branges-Rovnyak [dBRl), respectively) to solve matrix
versions of a number of classical interpolation problems. Enroute
we shall reinterpret de Branges' characterization of the first of
these spaces, when it is finite dimensional, in terms of matrix
equations of the Liapunov and Stein type and shall subsequently
draw some general conclusions on rational m x m matrix valued
functions which are "J unitary" a.e. on either the circle or the
line. We shall also make some connections with the notation of
displacement rank which has been introduced and extensively studied
by Kailath and a number of his colleagues as well as the one used
by Heinig and Rost [HR). The first of the two classes of spaces
alluded to above is distinguished by a reproducing kernel of the
special form K (>.) = J - U(>')JU(w)* (Ll) w Pw(>') , in
which J is a constant m x m signature matrix and U is an m x m J
inner matrix valued function over ~+, where ~+ is equal to either
the open unit disc ID or the open upper half plane (1)+ and
Pw(>') is defined in the table below.
R. S. PHILLIPS I am very gratified to have been asked to give this
introductory talk for our honoured guest, Israel Gohberg. I should
like to begin by spending a few minutes talking shop. One of the
great tragedies of being a mathematician is that your papers are
read so seldom. On the average ten people will read the
introduction to a paper and perhaps two of these will actually
study the paper. It's difficult to know how to deal with this
problem. One strategy which will at least get you one more reader,
is to collaborate with someone. I think Israel early on caught on
to this, and I imagine that by this time most of the analysts in
the world have collaborated with him. He continues relentlessly in
this pursuit; he visits his neighbour Harry Dym at the Weizmann
Institute regularly, he spends several months a year in Amsterdam
working with Rien Kaashoek, several weeks in Maryland with Seymour
Goldberg, a couple of weeks here in Calgary with Peter Lancaster,
and on the rare occasions when he is in Tel Aviv, he takes care of
his many students.
This book provides a careful treatment of the theory of algebraic
Riccati equations. It consists of four parts: the first part is a
comprehensive account of necessary background material in matrix
theory including careful accounts of recent developments involving
indefinite scalar products and rational matrix functions. The
second and third parts form the core of the book and concern the
solutions of algebraic Riccati equations arising from continuous
and discrete systems. The geometric theory and iterative analysis
are both developed in detail. The last part of the book is an
exciting collection of eight problem areas in which algebraic
Riccati equations play a crucial role. These applications range
from introductions to the classical linear quadratic regulator
problems and the discrete Kalman filter to modern developments in
HD*W*w control and total least squares methods.
This book is dedicated to the memory of Israel Gohberg (1928-2009)
- one of the great mathematicians of our time - who inspired
innumerable fellow mathematicians and directed many students. The
volume reflects the wide spectrum of Gohberg's mathematical
interests. It consists of more than 25 invited and peer-reviewed
original research papers written by his former students, co-authors
and friends. Included are contributions to single and multivariable
operator theory, commutative and non-commutative Banach algebra
theory, the theory of matrix polynomials and analytic vector-valued
functions, several variable complex function theory, and the theory
of structured matrices and operators. Also treated are canonical
differential systems, interpolation, completion and extension
problems, numerical linear algebra and mathematical systems theory.
R. S. PHILLIPS I am very gratified to have been asked to give this
introductory talk for our honoured guest, Israel Gohberg. I should
like to begin by spending a few minutes talking shop. One of the
great tragedies of being a mathematician is that your papers are
read so seldom. On the average ten people will read the
introduction to a paper and perhaps two of these will actually
study the paper. It's difficult to know how to deal with this
problem. One strategy which will at least get you one more reader,
is to collaborate with someone. I think Israel early on caught on
to this, and I imagine that by this time most of the analysts in
the world have collaborated with him. He continues relentlessly in
this pursuit; he visits his neighbour Harry Dym at the Weizmann
Institute regularly, he spends several months a year in Amsterdam
working with Rien Kaashoek, several weeks in Maryland with Seymour
Goldberg, a couple of weeks here in Calgary with Peter Lancaster,
and on the rare occasions when he is in Tel Aviv, he takes care of
his many students.
In this article we shall use two special classes of reproducing
kernel Hilbert spaces (which originate in the work of de Branges
[dB) and de Branges-Rovnyak [dBRl), respectively) to solve matrix
versions of a number of classical interpolation problems. Enroute
we shall reinterpret de Branges' characterization of the first of
these spaces, when it is finite dimensional, in terms of matrix
equations of the Liapunov and Stein type and shall subsequently
draw some general conclusions on rational m x m matrix valued
functions which are "J unitary" a.e. on either the circle or the
line. We shall also make some connections with the notation of
displacement rank which has been introduced and extensively studied
by Kailath and a number of his colleagues as well as the one used
by Heinig and Rost [HR). The first of the two classes of spaces
alluded to above is distinguished by a reproducing kernel of the
special form K (>.) = J - U(>')JU(w)* (Ll) w Pw(>') , in
which J is a constant m x m signature matrix and U is an m x m J
inner matrix valued function over ~+, where ~+ is equal to either
the open unit disc ID or the open upper half plane (1)+ and
Pw(>') is defined in the table below.
Thefollowing topics ofmathematical analysishavebeen developed in
the last?fty years:
thetheoryoflinearcanonicaldi?erentialequationswithperiodicHamilto-
ans, the theory of matrix polynomials with selfadjoint coe?cients,
linear di?er- tial and di?erence equations of higher order with
selfadjoint constant coe?cients, andalgebraicRiccati equations.All
of these theories, and others, arebased on r- atively recent
results of linear algebra in spaces with an inde?nite inner
product, i.e., linear algebra in which the usual positive de?nite
inner product is replaced by an inde?nite one. More concisely, we
call this subject inde?nite linear algebra. This book has the
structureof a graduatetext in which chaptersof advanced linear
algebra form the core. The development of our topics follows the
lines of a usual linear algebra course. However, chapters giving
comprehensive treatments of di?erential and di?erence equations,
matrix polynomials and Riccati equations are interwoven as the
necessary techniques are developed. The main source of material is
our earlier monograph in this ?eld: Matrices and Inde?nite Scalar
Products, 40]. The present book di?ers in objectives and
material.Somechaptershavebeenexcluded, othershavebeenadded,
andexercises have been added to all chapters. An appendix is also
included. This may serve as a summary and refresher on standard
results as well as a source for some less familiar material from
linear algebra with a de?nite inner product. The theory developed
here has become an essential part of linear algebra. This, together
with the many signi?cant areas of application, and the accessible
style, make this book useful for engineers, scientists and
mathematicians al
In this book the authors try to bridge the gap between the
treatments of matrix theory and linear algebra. It is aimed at
graduate and advanced undergraduate students seeking a foundation
in mathematics, computer science, or engineering. It will also be
useful as a reference book for those working on matrices and linear
algebra for use in their scientific work.
This scarce antiquarian book is a selection from Kessinger
Publishing's Legacy Reprint Series. Due to its age, it may contain
imperfections such as marks, notations, marginalia and flawed
pages. Because we believe this work is culturally important, we
have made it available as part of our commitment to protecting,
preserving, and promoting the world's literature. Kessinger
Publishing is the place to find hundreds of thousands of rare and
hard-to-find books with something of interest for everyone
This text covers several aspects and solutions of the problems of linear vibrating systems with a finite number of degrees of freedom. It offers a detailed account of the part of the theory of matrices necessary for efficient problem-solving, beginning with the first four chapters' focus on developing the necesary tools in matrix theory. The following chapters present numerical procedures for the relevant matrix formulations and the relevant theory of differential equations. The book is directed toward a wide audience of applied mathematicans, scientists, and engineers who are interested in these problems from either practical or theoretical points of view. Although mathematically sound, the treatment involves readers in a minimum of mathematical abstraction. A familiarity and facility with matrix theory is assumed, along with a knowlege of elementary calculus, including the rudiments of the theory of functions of a complex variable. Unabridged republication of the edition published by Pergamon Press, Oxford, 1966. Preface. Bibliographical Notes. References. Index.
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