Series: Universitext
2009, Approx. 345 p., Softcover
ISBN: 978-0-387-85468-7
Due: December 2008
About this textbook
Contains material unavailable elsewhere, including the full proof of Pontryagin Duality and the Plancherel Theorem
Authors emphasize Banach algebras as the cleanest way to get many fundamental results in harmonic analysis
Gentle pace, clear exposition, and clean proofs
The present book is intended as a text for a graduate course on abstract harmonic analysis and its applications. The book can be used as a follow up to Anton Deitmer's previous book, A First Course in Harmonic Analysis, or independently, if the students already have a modest knowledge of Fourier Analysis. In this book, among other things, proofs are given of Pontryagin Duality and the Plancherel Theorem for LCA-groups, which were mentioned but not proved in A First Course in Harmonic Analysis. Using Pontryagin duality, the authors also obtain various structure theorems for locally compact abelian groups. The book then proceeds with Harmonic Analysis on non-abelian groups and its applications to theory in number theory and the theory of wavelets.
Knowledge of set theoretic topology, Lebesgue integration, and functional analysis on an introductory level will be required in the body of the book. For the convenience of the reader, all necessary ingredients from these areas have been included in the appendices.
Professor Deitmar is Professor of Mathematics at the University of Tubingen, Germany. He is a former Heisenberg fellow and has taught in the U.K. for some years. Professor Echterhoff is Professor of Mathematics and Computer Science at the University of Munster, Germany.
Series: Birkhauser Advanced Texts / Basler Lehrbucher
Approx. 475 p., 2009, Approx. 475 p., Hardcover
ISBN: 978-3-7643-8993-2
Due: March 2009
Unifies two approaches traditionally different, one using essentially abstract functional analysis and the other based on techniques coming from partial differential equations
Obtains main exact observability results by combining functional analysis with various methods such as multipliers, Ingham-Beurling-type inequalities and Carleman estimates
Uses elliptic and the parabolic Carleman-type estimates that are worked out in detail, with an elementary construction of the necessary weight function
Self-contained
This book studies observation and control operators for linear systems where the free evolution of the state can be described by an operator semigroup on a Hilbert space. The emphasis is on well-posedness, observability and controllability properties. The abstract results are supported by a large number of examples coming mostly from partial differential equations. These examples are worked out in detail. This book is meant to be an elementary introduction in this theory. The first meaning of "elementary'' is that the text is aimed to be accessible to any reader familiar with linear algebra, calculus, the basics of Hilbert spaces and differential equations. We introduce everything needed on operator semigroups and most of the background used is summarized in the Appendices, often with proofs. The second meaning of "elementary'' is that we only cover results for which we can provide complete proofs. In our bibliographic comments we mention some of the more advanced results, for example those based on microlocal analysis.
Preface.- 1. Finite-dimensional Systems.- 2. Operator Semigroups.- 3. Semigroups of Contractions.- 4. Control and Observation Operators.- 5. Observability.- 6. Observation for the Wave Equation.- 7. Non-harmonic Fourier Series and Exact Observability.- 8. Observability for Parabolic Equations.- 9. Boundary Control Systems.- 10. Controllability.- Appendices.- References.
Series: Operator Theory: Advances and Applications , Preliminary entry 000
2009, Approx. 1000 p. 2-volume-set.
ISBN: 978-3-7643-9924-5
Due: April 2009
These two volumes contain peer-reviewed research and survey papers based on invited talks at the International Conference on Modern Analysis and Applications. The conference, which was dedicated to the 100th anniversary of the birth of Mark Krein, one of the greatest mathematicians of the 20th century, was held in Odessa, Ukraine, on April 9-14, 2007. The papers describe the contemporary development of subjects influenced by Krein, such as the theory of operators in Hilbert and Krein spaces, differential operators, applications of functional analysis in function theory, theory of networks and systems, mathematical physics and mechanics.
Researchers in operator theory, functional analysis, and integral equations
integral equations
2009, Approx. 280 p. 20 illus., Hardcover
ISBN: 978-0-387-88756-2
Due: April 2009
One of the first books to cover SAT-solvers and how they can be used in cryptanalysis; there are also chapters on finite field linear algebra and the cipher Keeloq
Excellent guide for advanced-level students, researchers and practitioners entering the algebraic cryptanalysis field
Bridges the gap between a course in cryptography and being able to read the cryptanalytic literature, among academics and industry practitioners
Algebraic Cryptanalysis is a guide for advanced-level students and researchers/practitioners entering this new field. This text bridges the gap between a course in cryptography, and being able to read the cryptanalytic literature. Algebraic Cryptanalysis also covers several chapters on finite field linear algebra and the equicomplexity of matrix operations.
This volume introduces several techniques, including linear systems of equations over finite fields, polynomial systems, along with how to adapt the latter to be solved by SAT-solvers. The cipher Keeloq, used in nearly all automobiles with remote key-less entry, is described as a running example, including the manipulation of the equations to enable their solution.
Designed for advanced-level students in computer science and mathematics as a secondary text or reference book. Also suitable for practitioners working for intelligence agencies or security companies. Of special interest to algebraic geometers interested in seeking more applied topics.
Advanced-level students in computer science and mathematics, as a secondary text or reference book; practitioners working for intelligence agencies or security companies; algebraic geometers interested in seeking more applied topics
Preface.- Introduction: How to Use this Book.- An Extended Example: Keeloq.- The Block-Cipher Keeloq and Algebraic Attacks.- The Fixed-Point Attack.- Polynomial Systems and Satisfiability.- 4 Strategies for Polynomial Systems.- Algorithms for Solving Polynomial Systems.- Converting MQ to CNF-SAT.- How Do SAT-Solvers Operate?.- Applying SAT-Solvers to Extension Fields of Low Degree.- Linear Systems.- Some Basic Facts about Linear Algebra over GF(2).- A Model for the Complexity of GF(2)-Operations.- On the Exponent of Certain Matrix Operations.- The Method of Four Russians.- An Impractical Method of Accelerating Matrix Operations in Rings of Finite Size.- Appendix.- Index.