Series: Lecture Notes of the Unione Matematica Italiana , Vol. 4
2008, VIII, 189 p., Softcover
ISBN: 978-3-540-74708-6
About this book
Various applications of equimeasurable function rearrangements to the ''best constant"-type problems are considered in this volume. Several classical theorems are presented along with some very recent results. In particular, the text includes a product-space extension of the Rising Sun lemma, a product-space version of the John-Nirenberg inequality for bounded mean oscillation (BMO) functions with sharp exponent, a refinement of the Gurov-Reshetnyak lemma, sharp embedding theorems for Muckenhoupt, Gurov-Reshetnyak, reverse Holder, and Gehring classes, etc. This volume is interesting for graduate students and mathematicians involved with these topics.
Written for:
Researchers and graduate students
Keywords:
42B25, 46E30
Gurov ? Reshetnyak classes
bounded mean oscillation (BMO)
equimeasurable rearrangements of functions
mean oscillation
reverse Holder inequalities
Table of contents
Series: Lecture Notes in Mathematics , Vol. 1923
2008, Approx. 280 p., Softcover
ISBN: 978-3-540-74447-4
Due: October 9, 2007
About this book
Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modelling complex phenomena and making beautiful decisions. The subject has attracted researchers from several areas of mathematics and other related fields like economics and finance. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods. Useful because of the current availability of high frequency data is the study of refined asymptotic properties of several estimators when the observation time length is large and the observation time interval is small. Also space time white noise driven models, useful for spatial data, and more sophisticated non-Markovian and non-semimartingale models like fractional diffusions that model the long memory phenomena are examined in this volume.
Table of contents
Preface.- 1.Parametric Stochastic Differential Equations.- Part I: Continuous Sampling.- 2.Rates of Weak Convergence of Estimators in Homogeneous Diffusions. -3.Large Deviations for Estimators in Homogeneous Diffusions.- 4.Local Asymptotic Mixed Normality for Nonhomogeneous Diffusions.- 5.Bayes and Sequential Estimation in Stochastic PDEs.- 6.Maximum Likelihood Estimation in Fractional Diffusions.- Part II: Discrete Sampling.- 7.Approximate Maximum Likelihood Estimation in Nonhomogeneous Diffusions.- 8.Rates of Weak Convergence of Estimators in the Ornstein-Uhlenbeck Process.- 9.Local Asymptotic Normality for Discretely Observed Homogeneous Diffusions.- 10.Estimating Functions for Discretely Observed Homogeneous Diffusions.- Bibliography.- Index.
Series: Lecture Notes in Mathematics , Vol. 1924
2008, XIII, 221 p., Softcover
ISBN: 978-3-540-74582-2
Due: October 16, 2007
About this book
Littlewood-Paley theory is an essential tool of Fourier analysis, with applications and connections to PDEs, signal processing, and probability. It extends some of the benefits of orthogonality to situations where orthogonality doesnft really make sense. It does so by letting us control certain oscillatory infinite series of functions in terms of infinite series of non-negative functions. Beginning in the 1980s, it was discovered that this control could be made much sharper than was previously suspected. The present book tries to give a gentle, well-motivated introduction to those discoveries, the methods behind them, their consequences, and some of their applications.
Table of contents
Some Assumptions.- An Elementary Introduction.- Exponential Square.- Many Dimensions.- Smoothing.- The Calderon Reproducing Formula I.- The Calderon Reproducing Formula II.- The Calderon Reproducing Formula III.- Schroedinger Operators.- Some Singular Integrals.- Spaces.- Goodbye to Good-Lambda.- A Fourier-Multiplier Theorem.- Vector-Valued Inequalities.- Random Pointwise Errors.- Index.- References.
Series: Lecture Notes in Mathematics , Vol. 1926
2008, VIII, 277 p., Softcover
ISBN: 978-3-540-74774-1
Due: October 9, 2007
About this book
Main theme of this volume is the stability of nonautonomous differential equations, with emphasis on the Lyapunov stability of solutions, the existence and smoothness of invariant manifolds, the construction and regularity of topological conjugacies, the study of center manifolds, as well as their reversibility and equivariance properties. Most results are obtained in the infinite-dimensional setting of Banach spaces. Furthermore, the linear variational equations are always assumed to possess a nonuniform exponential behavior, given either by the existence of a nonuniform exponential contraction or a nonuniform exponential dichotomy. The presentation is self-contained and has unified character. The volume contributes towards a rigorous mathematical foundation of the theory in the infinite-dimension setting, and may lead to further developments in the field. The exposition is directed to researchers as well as graduate students interested in differential equations and dynamical systems, particularly in stability theory.
Table of contents
Preface.- Introduction.- Part I Exponential dichotomies.- Exponential dichotomies and basic properties.- Robustness of nonuniform exponential dichotomies.- Part II Stable manifolds and topological conjugacies.- Lipschitz stable manifolds.- Smooth stable manifolds in R^n.- Smooth stable manifolds in Banach spaces.- A nonautonomous Grobman?Hartman theorem.- Part III Center manifolds, symmetry and reversibility.- Center manifolds in Banach spaces.- Reversibility and equivariance in center manifolds.- Part IV Lyapunov regularity and stability theory.- Lyapunov regularity and exponential dichotomies.- Lyapunov regularity in Hilbert spaces.- Stability of nonautonomous equations in Hilbert spaces.- References.- Index
2008, XVIII, 689 p. With CD-ROM., Hardcover
ISBN: 978-3-540-73541-0
Due: November 6, 2007
About this textbook
Highly popular, hands-on book on
First handbook/tutorial to extensively deal with SINGULAR
Top quality book for top quality software
From the reviews:
"cIt is certainly no exaggeration to say that Greuel and Pfister's A Singular Introduction to Commutative Algebra aims to lead a further stage in the computational revolution in commutative algebra, in which computational methods and results become central to how the subject is taught and learned. [c] Among the great strengths and most distinctive features of Greuel and Pfister's book is a new, completely unified treatment of the global and local theories. The realization that the two cases could be combined to this extent was decisive in the design of the Singular system, making it one of the most flexible and most efficient systems of its type. The authors present the first systematic development of this unified approach in a textbook here, and this aspect alone is almost worth the price of admission. Another distinctive feature of this book is the degree of integration of explicit computational examples into the flow of the text. Strictly mathematical components of the development (often quite terse and written in a formal "theorem-proof" style) are interspersed with parallel discussions of features of Singular and numerous Singular examples giving input commands, some extended programs in the Singular language, and output. [c] Yet another strength of Greuel and Pfister's book is its breadth of coverage of theoretical topics in the portions of commutative algebra closest to algebraic geometry, with algorithmic treatments of almost every topic. A synopsis of the table of contents will make this clear. [c] Greuel and Pfister have written a distinctive an highly useful book that should be in the library of every commutative algebrais and algebraic geometer, expert and novice alike. I hope that it achieves the educational impact it deserves."
Table of contents
1 Rings, Ideals and Standard Bases.- 2. Modules.- 3. Noether Normalization and Applications.- 4. Primary Decomposition and Related Topics.- 5. Hilbert Function and Dimension.- 6. Complete Local Rings.- 7. Homological Algebra.- Appendix A. Geometric Background.- B. Polynomial Factorization.- C. SINGULAR - A Short Introduction.- References.- Glossary.- Index.