Series : Probability and its Applications
2004, Approx. 300 p. 15 illus., Hardcover
ISBN: 1-85233-761-3
About this book
Safety critical and high-integrity systems, such as industrial
plants and economic systems can be subject to abrupt changes -
for instance due to component or interconnection failure, and
sudden environment changes etc. Combining probability and
operator theory, Discrete-Time Markov Jump Linear Systems
provides a unified and rigorous treatment of recent results for
the control theory of discrete jump linear systems, which are
used in these areas of application. The book is designed for
experts in linear systems with Markovian jump parameters, but
will also be the first book for specialists in stochastic control
to present stochastic control problems for which an explicit
solution is possible - making the book suitable for course use.
Table of contents
Preface.- Markovian Jump Linear Systems.- Background Material.-
On Stability.- Optimal Control.- Linear Filtering.- Quadratic
Optimal Control with Partial Information.- H2- Control.- Design
Techniques and Examples.- Appendix A: Coupled Algebraic Riccati
Equations.- Appendix B: Auxiliary Results for the Linear
Filtering Problem with (k) Unknown.- Appendix C: Auxiliary
Results for the H2 Control Problem.- Notation and Corrections.-
References.
Series : Classics in Mathematics
Reprint of the 1st ed. Berlin Heidelberg New York 1986, 2005,
XIV, 465 p., Softcover
ISBN: 3-540-22614-1
About this book
From the reviews: "The author, [...], has written a book
which will be of service to all who are interested in this by now
vast subject. [...] This is a book of many virtues: mathematical,
historical, and pedagogical. Parts of it could be used for a
graduate complex manifolds course.J.A. Carlson in Mathematical
Reviews, 1987 "There are many mathematicians, or even
physicists, who would find this book useful and accessible, but
its distinctive attribute is the insight it gives into a
brilliant mathematician's work. [...] It is intriguing to sense
between the lines Spencer's optimism, Kodaira's scepticism or the
shadow of Grauert with his very different methods, as it is to
hear of the surprises and ironies which appeared on the way. Most
of all it is a piece of work which shows mathematics as lying
somewhere between discovery and invention, a fact which all
mathematicians know, but most inexplicably conceal in their work."N.J.
Hitchin in the Bulletin of the London Mathematical Society, 1987
Table of contents
Holomorphic Functions.- Complex Manifolds.- Differential Forms,
Vector Bundles, Sheaves.- Infinitesimal Deformation.- Theorem of
Existence.- Theorem of Completeness.- Theorem of Stability.-
Appendix: Elliptic Partial Differential Operators on a Manifold
by Daisuke Fujiwara.- Bibliography.- Index.
Series : Classics in Mathematics
Reprint of the 1st ed. Berlin Heidelberg New York 1985, 2005,
XIX, 488 p., Softcover
ISBN: 3-540-22617-6
About this book
From the reviews "[...] This book presents a complete
treatment of a new class of random processes, which have been
studied intensively during the last fifteen years. None of this
material has ever appeared in book form before. cThe high
quality of this work, [...] , makes a fascinating subject and its
open problem as accessible as possible. [...]" F.L. Spitzer
in Mathematical Reviews, 1986 "[...] However, it can be said
that the author has succeeded in what even experts are seldom
able to achieve: To write a clearcut and inspiring book on his
favorite subject which meets most, if not all requirements which
can be imposed on a comprehensive text on an important new field.
The author can be congratulated on his excellent presentation of
the theory of interacting particle systems. The book is highly
recommended to everyone who works on or is interested in this
subject: to probabilists, physicists and theoretical biologists.
[...]" G. Rosenkranz in Methods of Information in Medicine,
1986
Table of contents
Introduction.- The Construction, and Other General Results.- Some
Basic Tools.- Spin System.- Stochastic Ising Models.- The Voter
Model.- The Contract Process.- Neareast-Particle Systems.- The
Exclusion Process.- Linear Systems with Values in [0, infinity)s.-
Bibliography.- Index.
2005, XII, 180 p., Hardcover
ISBN: 0-387-21978-1
About this book
This book aims to promote constructive mathematics not by
defining it or formalizing it but by practicing it. This means
that its definitions and proofs use finite algorithms, not
`algorithms' that require surveying an infinite number of
possibilities to determine whether a given condition is met. The
topics covered derive from classic works of nineteenth century
mathematics---among them Galois' theory of algebraic equations,
Gauss's theory of binary quadratic forms and Abel's theorem about
integrals of rational differentials on algebraic curves. It is
not surprising that the first two topics can be treated
constructively---although the constructive treatments shed a
surprising amount of light on them---but the last topic,
involving integrals and differentials as it does, might seem to
call for infinite processes. In this case too, however, finite
algorithms suffice to define the genus of an algebraic curve, to
prove that birationally equivalent curves have the same genus,
and to prove the Riemann-Roch theorem. The main algorithm in this
case is Newton's polygon, which is given a full treatment. Other
topics covered include the fundamental theorem of algebra, the
factorization of polynomials over an algebraic number field, and
the spectral theorem for symmetric matrices. Harold M. Edwards is
Emeritus Professor of Mathematics at New York University. His
previous books are Advanced Calculus (1969, 1980, 1993),
Riemann's Zeta Function (1974, 2001), Fermat's Last Theorem (1977),
Galois Theory (1984), Divisor Theory (1990) and Linear Algebra (1995).
Readers of his Advanced Calculus will know that his preference
for constructive mathematics is not new.
Table of contents
Preface * Synopsis * PART 1: A Fundamental Theorem * General
Arithmetic * A Fundamental Theorem * Roots Field (Simple
Algebraic Extensions) * Factorization of Polynomials with Integer
Coefficients * A Factorization Algorithm * Validation of the
Factorization Algorithm * About the Factorization Algorithm *
Proof of the Fundamental Theorem * Minimal Splitting Polynomials
* PART 2: Topics in Algebra * Galois' Fundamental Theorem *
Algebraic Quantities * Adjunctions and the Factorization of
Polynomials * Symmetric Polynomials and the Splitting Field of
x^n + c_1x^{n-1} + ... + c_n * A Fundamental Theorem of Divisor
Theory * PART 3: Some Quadratic Problems * Hypernumbers * Modules
* The Class Semigroup * Multiplication of Modules and Module
Classes * Is A a Square Mod p? * Gauss's Composition of Forms *
The Construction of Compositions * PART 4: The Genus of an
Algebraic Curve * Abel's Memoir * Euler's Addition Formula * An
Algebraic Definition of the Genus * Newton's Polygon *
Determination of the Genus * Holomorphic Differentials * The
Riemann-Roch Theorem * The Genus is a Birational Invariant * PART
5: Miscellany * On the So-Called Fundamental Theorem of Algebra *
Proof by Contradiction and the Sylow Theorems * Overview of
'Linear Algebra' * The Spectral Theorem * Kronecker as One of E.T.
Bell's 'Men of Mathematics' * References
Series : Classics in Mathematics
Reprint of the 1st ed. Berlin Heidelberg New York 1983, 2005,
XII, 392 p., Softcover
ISBN: 3-540-22516-1
About this book
Vol. I of Lars Hormander's 4-volume treatise was an exposition of
the theory of distributions and Fourier analysis preparing for
the study of linear partial differential operators. The present
Vol. II is mainly devoted to operators with constant coefficients.
An analysis of the existence and regularity of (fundamental)
solutions in the first two chapters is followed by a thorough
study of the Cauchy problem. One chapter is devoted to the
spectral theory of short range perturbations of operators with
constant coefficients, and another presents Fourier-Laplace
representations of solutions of homogeneous differential
equations with constant coefficients. The last chapter is a study
of the closely related subject of convolution operators.
Table of contents
Introduction.- Existence and Approximation of Solutions of
Differential Equations.- Interior Regularity of Solutions of
Differential Equations.- The Cauchy and Mixed Problems.-
Differential Operators of Constant Strength.- Scattering Theory.-
Analytic Function Theory and Differential Equations.- Convolution
Equations.- Appendix A: Some Algebraic Lemmas.- Bibliography.-
Index.- Index of Notation.
Series : Graduate Texts in Mathematics , Vol. 226
2004, Approx. 290 p., Hardcover
ISBN: 0-387-22036-4
About this textbook
The book presents a modern theory of holomorphic function spaces
in the open unit ball. Spaces discussed include the Bergman
spaces, the Hardy spaces, the Bloch space, BMOA, the Dirichlet
space, the Besov spaces, and the Lipschitz spaces. Most proofs in
the book are new and simpler than the existing proofs in the
literature. The central idea in almost all these proofs is based
on integral representations of holomorphic functions and
elementary properties of the Bergman kernel, the Bergman metric,
and the automorphism group.
Table of contents
Preliminaries.- Bergman Spaces.- The Bloch Space.- Hardy Spaces.-
Functions of Bounded Mean Oscillation.- Besov Spaces.- Lipschitz
Spaces.- References.- Index.