Yitzhak Katznelson

An Introduction to Harmonic Analysis, 3rd Edition

Publication is planned for February 2004 | Hardback | 300 pages | ISBN: 0-521-83829-0
Publication is planned for February 2004 | Paperback | 300 pages | ISBN: 0-521-54359-2

First published in 1968, An Introduction to Harmonic Analysis has firmly established itself as a classic text and a favorite for students and experts alike. Professor Katznelson starts the book with an exposition of classical Fourier series. The aim is to demonstrate the central ideas of harmonic analysis in a concrete setting, and to provide a stock of examples to foster a clear understanding of the theory. Once these ideas are established, the author goes on to show that the scope of harmonic analysis extends far beyond the setting of the circle group, and he opens the door to other contexts by considering Fourier transforms on the real line as well as a brief look at Fourier analysis on locally compact abelian groups. This new edition has been revised by the author, to include several new sections and a new appendix.

Contents

1. Fourier Series on T; 2. The Convergence of Fourier Series; 3. The Conjugate Function; 4. Interpolation of Linear Operators; 5. Lacunary Series and Quasi-analytic Classes; 6. Fourier Transfomrs on the Line; 7. Fourier Analysis on Locally Compact Abelian Groups; 8. Comutative Banach Algebras; A. Vector-Valued Functions; B. Probabilistic Methods.

Donald T. Greenwood

Advanced Dynamics

November 2003 | Hardback | 434 pages 115 exercises 168 figures | ISBN: 0-521-82612-8

Advanced Dynamics is a broad and detailed description of the analytical tools of dynamics as used in mechanical and aerospace engineering. The strengths and weaknesses of various approaches are discussed, and particular emphasis is placed on learning through problem solving. The book begins with a thorough review of vectorial dynamics and goes on to cover Lagrange’s and Hamilton’s equations as well as less familiar topics such as impulse response, and differential forms and integrability. Techniques are described that provide a considerable improvement in computational efficiency over the standard classical methods, especially when applied to complex dynamical systems. The treatment of numerical analysis includes discussions of numerical stability and constraint stabilization. Many worked examples and homework problems are provided. The book is intended for use on graduate courses on dynamics, and will also appeal to researchers in mechanical and aerospace engineering.

Contents

1. Introduction to particle dynamics; 2. Lagrange’s and Hamilton’s equations; 3. Kinematics and dynamics of a rigid body; 4. Equations of motion: differential approach; 5. Equations of motion: integral approach; 6. Introduction to numerical methods; Appendix.

Stephen Boyd, Lieven Vandenberghe

Convex Optimization

Publication is planned for January 2004 | Hardback | 736 pages 337 exercises 178 figures | ISBN: 0-521-83378-7

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained mimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance, and economics.

Contents

Preface; 1. Introduction; Part I. Theory: 2. Convex sets; 3. Convex functions; 4. Convex optimization problems; 5. Duality; Part II. Applications: 6. Approximation and fitting; 7. Statistical estimation; 8. Geometrical problems; Part III. Algorithms: 9. Unconstrained minimization; 10. Equality constrained minimization; 11. Interior-point methods; Appendices.

Edited by John D. Barrow, Paul C. W. Davies, Charles L. Harper

Science and Ultimate Reality
Quantum Theory, Cosmology and Complexity

Publication is planned for March 2004 | Hardback | 744 pages 53 line diagrams 8 half-tones | ISBN: 0-521-83113-X

This volume provides a fascinating snapshot of the future of physics, covering fundamental physics, at the frontiers of research. It comprises a wide variety of contributions from leading thinkers in the field, inspired by the pioneering work of John A. Wheeler. Quantum theory represents a unifying theme within the book, along with topics such as the nature of physical reality, the arrow of time, models of the universe, superstrings, gravitational radiation, quantum gravity and cosmic inflation. Attempts to formulate a final unification of physics are discussed, along with the existence of hidden dimensions of space, space-time singularities, hidden cosmic matter, and the strange world of quantum technology.

Contributors

John A. Wheeler, Kenneth W. Ford, Paul C. W. Davies, David Deutsch, Bryce S. DeWitt, Freeman J. Dyson, Lucien Hardy, Juan C. Maldacena, Juan Pablo Paz, H. Dieter Zeh, Wojciech H. Zurek, Raymond Y. Chiao, Serge Haroche, Paul G. Kwiat, Berthold-Georg Englert, Hideo Mabuchi, Christopher R. Monroe, Aephraim M. Steinberg, Andreas Albrecht, John D. Barrow, Andrei Linde, Joao Magueijo, Fotini G. Markopoulou Kalamara, Lisa J. Randall, Lee Smolin, Max Tegmark, Philip D. Clayton, George F. R. Ellis, Marcelo Gleiser, Stuart A. Kauffman, Shoucheng Zhang, Anton Zeilinger, Jaroslav Pelikan

Tomas Ortin

Gravity and Strings

Publication is planned for March 2004 | Hardback | 671 pages 28 line diagrams 13 tables | ISBN: 0-521-82475-3

One appealing feature of string theory is that it provides a theory of quantum gravity. Gravity and Strings is a self-contained, pedagogical exposition of this theory, its foundations and its basic results. In Part I, the foundations are traced back to the very early special-relativistic field theories of gravity, showing how such theories lead to general relativity. Gauge theories of gravity are then discussed and used to introduce supergravity theories. In Part II, some of the most interesting solutions of general relativity and its generalizations are studied. The final Part presents and studies string theory from the effective action point of view, using the results found earlier in the book as background. This unique book will be useful as a reference book for graduate students and researchers, as well as a complementary textbook for courses on gravity, supergravity and string theory.

Contents

Part I. Introduction to Gravity and Supergravity: 1. Differential geometry; 2. Noether’s theorems; 3. A perturbative introduction to GR; 4. Action principles for gravity; 5. N = 1, 2, d = 4 Supergravities; 6. Conserved charges in GR; Part II. Gravitating Point-Particles: 7. The Schwarzschild black hole; 8. The Reissner-Nordstrom BH; 9. The Taub-NUT solution; 10. Gravitational pp-waves; 11. The Kaluza-Klein black hole; 12. Dilaton and dilaton/axion BHs; 13. Unbroken supersymmetry; Part III. Gravitating Extended Objects of String Theory: 14. String theory; 15. The string effective action and T duality; 16. From eleven to four dimensions; 17. The type IIB superstring and type II T duality; 18. Extended objects; 19. The extended objects of string theory; 20. String black holes in four and five dimensions; Appendix A. Lie groups, symmetric spaces and Yang-Mills fields; Appendix B. Gamma matrices and spinors; Appendix C. n-Spheres; Appendix D. Palatini’s identity; Appendix E. Conformal rescalings; Appendix F. Connections and curvature components; Appendix G. The harmonic operator on R3 x S 1; References; Index.