Series: Universitext
2010, Approx. 340 p. 25 illus., Softcover
ISBN: 978-1-4419-1220-6
Due: December 2009
Traditional logic as a part of philosophy is one of the oldest scientific disciplines and can be traced back to the Stoics and to Aristotle. Mathematical logic, however, is a relatively young discipline and arose from the endeavors of Peano, Frege, and others to create a logistic foundation for mathematics. It steadily developed during the twentieth century into a broad discipline with several sub-areas and numerous applications in mathematics, informatics, linguistics and philosophy.
This book treats the most important material in a concise and streamlined fashion. The third edition is a thorough and expanded revision of the former. Although the book is intended for use as a graduate text, the first three chapters can easily be read by undergraduates interested in mathematical logic. These initial chapters cover the material for an introductory course on mathematical logic, combined with applications of formalization techniques to set theory. Chapter 3 is partly of descriptive nature, providing a view towards algorithmic decision problems, automated theorem proving, non-standard models including non-standard analysis, and related topics.
The remaining chapters contain basic material on logic programming for logicians and computer scientists, model theory, recursion theory, Godelfs Incompleteness Theorems, and applications of mathematical logic. Philosophical and foundational problems of mathematics are discussed throughout the text. Each section of the seven chapters ends with exercises some of which of importance for the text itself. There are hints to most of the exercises in a separate file Solution Hints to the Exercises which is not part of the book but is available from the authorfs website.
Preface.- Introduction.- Notation.- Propositional Logic.- First-Order Logic.- Complete Logical Calculi.- Foundations of Logical Programming.- Elements of Model Theory.- Incompleteness and Undecidability.- On the Theory of Self-Reference.- Bibliography.- Index of Terms and Names.- Index of Symbols.-
Series: Pseudo-Differential Operators , Preliminary entry 5
2010, Approx. 400 p., Softcover
ISBN: 978-3-7643-9991-7
Due: January 2010
"Deformation quantization" is a mathematical theory which provides an alternative approach to quantum mechanics. It has ramifications in both pure mathematics and physics. This book gives a novel approach to the subject by using pseudo-differential methods ("Bopp quantization") where the theory of modulation spaces plays a central role.
Mathematicians working in partial differential equations, symplectic geometry, operator theory; mathematical physicists working in quantum mechanics.
1. Introduction.- 2. Weyl Calculus.- 3. Bopp Pseudodifferential Operators.- 4. The Uncertainty Principle.- 5. Deformation Quantization.- 6. Symplectic Covariance Properties.- 7. The Shubin Symbol Classes.- 8. Modulation spaces.- 9. Global Hypoellipticity.- 10. Spectral Properties.- 11. Semiclassical Theory.- Bibliography.- Index.
Series: Operator Theory: Advances and Applications , Vol. 198
2010, Approx. 330 p., Hardcover
ISBN: 978-3-0346-0179-5
Due: January 2010
The present book is a memorial volume devoted to Peter Jonas. It displays recent advances in modern operator theory in Hilbert and Krein spaces and contains a collection of original research papers written by many well-known specialists in this field. The papers contain new results for problems close to the area of research of Peter Jonas: Spectral and perturbation problems for operators in inner product spaces, generalized Nevanlinna functions and definitizable functions, scattering theory, extension theory for symmetric operators, fixed points, hyperbolic matrix polynomials, moment problems, indefinite spectral and Sturm-Liouville problems, and invariant subspace problems.
This book is written for researchers and postgraduates interested in functional analysis and differential operators.
Researchers and postgraduates interested in operator theory and functional analysis
Series: Operator Theory: Advances and Applications , Preliminary entry 559
2010, Approx. 650 p., Hardcover
ISBN: 978-3-0346-0157-3
Due: April 2010
This is the first volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The purpose is to bring in one volume many important original results of cutting edge research as well as authoritative review of recent achievements, challenges, and future directions in the area of operator theory and its applications.
Researchers in operator theory and related fields