Series: Applied and Numerical Harmonic Analysis
2008, Approx. 208 p. 40 illus., Hardcover
ISBN: 978-0-8176-4737-7
Due: May 2008
About this book
This book develops theory and algorithms leading to systematic waveform design in time-frequency space. The key tool employed in the work is the Zak transform, which provides a two-dimensional image for sequences, the Fourier transform, convolution, and correlation, and allows for the design of sequences directly in Zak space.
Topics and Features:
* Rigorous mathematical development of the theory is illustrated with many examples.
* Numerous tables compare signal sets satisfying good correlation properties attainable by standard communication theory methods versus Zak space methods.
* Application areas covered include pulse radars and sonars, multibeam radar and sonar imaging systems, remote dielectric material identification, and code division multiple-access communication systems.
* A variety of mathematical and application-oriented open problems are discussed.
Ideal Sequence Design in Time-Frequency Space is an excellent reference text for graduate students, researchers, and engineers in radar, sonar, and communication systems. The work may also be used as a supplementary textbook for a graduate course or seminar on sequence design in time-frequency space.
Table of contents
Preface.- Introduction.- Permutations and Permutation Matrices.- Finite Fourier Transform.- Convolution and Correlation.- Discrete Chirps.- Zak Transform.- Zak Space Correlation Formula.- Zak Space Representation of Chirps.- Permutations.- Permutation Sequences.- Modulation.- Sequence Sets.- Echo Analysis.- Sequence Shaping.- Problems.- References.- Index.
Series: IFSR International Series on Systems Science and Engineering ,
Vol. 25
2008, Approx. 400 p. 25 illus., Hardcover
ISBN: 978-0-387-76851-9
Due: June 2008
About this textbook
Generalized measure theory emerged from the classical measure theory by the process of generalization. Generalized measures are set functions that, contrary to classical measures, are not required to satisfy the requirement of additivity. This generalization significantly expands the applicability of measure theory and presents a way to overcome the current limitations of classical measure theory by providing tools to deal with problems in a more realistic way.
This book provides a comprehensive treatment of generalized measure theory. It covers important results on lower and upper integrals, fuzzification of generalized measure and new applications of the theory. The topics unfold systematically beginning with the preliminaries and introductory ideas before proceeding to a detailed treatment of the subject. Numerous examples motivate the theory and exercises at the end of the chapter provide practice to the student. Two appendices at the end of the book provide a glossary of key concepts and symbols.
This textbook is written for a junior/senior undergraduate or graduate course in mathematics as well as those areas of science and engineering where measure theory or classical probability theory have been employed. It can also be used for self-study and will be of interest to researchers in this area.
Table of contents
Preface.- Introduction.- Preliminaries.- Basic Ideas of Generalized Measure Theory.- Special Area of Generalized Measure Theory.- Extensions.- Structural Characteristics.- Measurable Functions on Monotone Measure Space.- Integration.- Sugeno Integrals.- Pan-Intergrals.- Choquet Integral.- Upper and Lower Integrations.- Constructing Generalized Measures.- Fuzzification in Generalized Measure Theory.- Applications of Generalized Measure Theory.- Bibliography.- Appendix A. Glossary of Key Concepts.- Appendix B. Glossary of Symbols.- Name Index.- Subject Index
Series: Operator Theory: Advances and Applications , Vol. 181
2008, Approx. 452 p., Hardcover
ISBN: 978-3-7643-8683-2
Due: May 2008
About this book
This book is composed of three survey lecture courses and some twenty invited research papers presented to WOAT 2006 - the International Summer School and Workshop on Operator Algebras, Operator Theory and Applications, which was held at Lisbon in September 2006. The volume reflects recent developments in the area of operator algebras and their interaction with research fields in complex analysis and operator theory. The lecture courses contain: an introduction to two classes of non-selfadjoint operator algebras, the generalized analytic Toeplitz algebras associated with the Fock space of a graph and subalgebras of graph C*-algebras; three topics on numerical functional analysis that are the cornerstones in asymptotic spectral theory: stability, fractality and Fredholmness; a survey concerning Hilbert spaces of holomorphic functions on Hermitian symmetric domains of arbitrary rank and dimension, in relation to operator theory, harmonic analysis and quantization.
Table of contents
Editorial Introduction.- Program.- List of Participants.- Lectures of the Summer School (Stephen C. Power, Bernd Silbermann, Harald Upmeier).- Contributions to the Workshop
Series: Operator Theory: Advances and Applications , Vol. 183
2008, Approx. 400 p., Hardcover
ISBN: 978-3-7643-8725-9
Due: June 2008
About this book
This book is devoted to the detailed study of the recently discovered commutative C*-algebras of Toeplitz operators on the Bergman space over the unit disk. The key point to understand their structure and classify them surprisingly lies in the hyperbolic geometry of the unit disk. We develop as well a number of important problems whose successful solution was made possible and is based on the specific features of the Toeplitz operators from these commutative algebras.
Table of contents
1. Prologue.- 2. Bergman and Poly-Bergman Spaces.- 3. Bergman-Type Spaces on the Unit Disk.- 4. Toeplitz Operators with Commutative Symbol Algebras.- 5. Toeplitz Operators on the Unit Disk with Radial Symbols.- 6. Toeplitz Operators with Homogeneous Symbols.- 7. Anatomy of the Algebra Generated by Toeplitz Operators.- 8. Toeplitz Operators and Hyperbolic Geometry.- 9. Weighted Bergman spaces.- 10. Commutative Algebras of Toeplitz Operators.- 11. Dynamics of Properties, Radial Symbols.- 12. Dynamics of Properties, Parabolic case.- 13. Dynamics of Properties, Hyperbolic case.- Appendices.- References.- Index.
Series: Progress in Mathematics , Vol. 268
2008, Approx. 200 p., Hardcover
ISBN: 978-3-7643-8714-3
Due: September 2008
About this book
Studies the main tool that is used for creating spaces of positive or nonnegative curvature
As yet, there is no comprehensive survey of this topic
Riemannian manifolds, particularly those with positive or nonnegative curvature, are constructed from only a handful by means of metric fibrations or deformations thereof. This text documents some of these constructions, many of which have only appeared in journal form. The emphasis is less on the fibration itself and more on how to use it to either construct or understand a metric with curvature of fixed sign on a given space.
Table of contents
Preface.- 1. Submersions, Foliations and Metrics.- 2.- Basic Constructions and Examples.- 3. Open Manifolds with Curvature at least 0.- 4. Metric Foliations in Space Forms.- Bibliography.