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Author: James Alexander Shohat
Publisher: American Mathematical Soc.
ISBN: 0821815016
Category : Mathematics
Languages : en
Pages : 160
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Book Description
The book was first published in 1943 and then was reprinted several times with corrections. It presents the development of the classical problem of moments for the first 50 years, after its introduction by Stieltjes in the 1890s. In addition to initial developments by Stieltjes, Markov, and Chebyshev, later contributions by Hamburger, Nevanlinna, Hausdorff, Stone, and others are discussed. The book also contains some results on the trigonometric moment problem and a chapter devoted to approximate quadrature formulas.
Author: James Alexander Shohat
Publisher: American Mathematical Soc.
ISBN: 0821815016
Category : Mathematics
Languages : en
Pages : 160
Get Book Here
Book Description
The book was first published in 1943 and then was reprinted several times with corrections. It presents the development of the classical problem of moments for the first 50 years, after its introduction by Stieltjes in the 1890s. In addition to initial developments by Stieltjes, Markov, and Chebyshev, later contributions by Hamburger, Nevanlinna, Hausdorff, Stone, and others are discussed. The book also contains some results on the trigonometric moment problem and a chapter devoted to approximate quadrature formulas.
Author: Konrad Schmüdgen
Publisher: Springer
ISBN: 3319645463
Category : Mathematics
Languages : en
Pages : 530
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Book Description
This advanced textbook provides a comprehensive and unified account of the moment problem. It covers the classical one-dimensional theory and its multidimensional generalization, including modern methods and recent developments. In both the one-dimensional and multidimensional cases, the full and truncated moment problems are carefully treated separately. Fundamental concepts, results and methods are developed in detail and accompanied by numerous examples and exercises. Particular attention is given to powerful modern techniques such as real algebraic geometry and Hilbert space operators. A wide range of important aspects are covered, including the Nevanlinna parametrization for indeterminate moment problems, canonical and principal measures for truncated moment problems, the interplay between Positivstellensätze and moment problems on semi-algebraic sets, the fibre theorem, multidimensional determinacy theory, operator-theoretic approaches, and the existence theory and important special topics of multidimensional truncated moment problems. The Moment Problem will be particularly useful to graduate students and researchers working on moment problems, functional analysis, complex analysis, harmonic analysis, real algebraic geometry, polynomial optimization, or systems theory. With notes providing useful background information and exercises of varying difficulty illustrating the theory, this book will also serve as a reference on the subject and can be used for self-study.
Author: James Alexander Shohat
Publisher: American Mathematical Society(RI)
ISBN:
Category : Mathematics
Languages : en
Pages : 168
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Book Description
Presents the development of the classical problem of moments for the first 50 years, after its introduction by Stieltjes in the 1890s. This book discusses the initial developments by Stieltjes, Markov, and Chebyshev, and later contributions by Hamburger, Nevanlinna, Hausdorff, and Stone.
Author: Jean-Bernard Lasserre
Publisher: World Scientific
ISBN: 1848164467
Category : Mathematics
Languages : en
Pages : 384
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Book Description
1. The generalized moment problem. 1.1. Formulations. 1.2. Duality theory. 1.3. Computational complexity. 1.4. Summary. 1.5. Exercises. 1.6. Notes and sources -- 2. Positive polynomials. 2.1. Sum of squares representations and semi-definite optimization. 2.2. Nonnegative versus s.o.s. polynomials. 2.3. Representation theorems : univariate case. 2.4. Representation theorems : mutivariate case. 2.5. Polynomials positive on a compact basic semi-algebraic set. 2.6. Polynomials nonnegative on real varieties. 2.7. Representations with sparsity properties. 2.8. Representation of convex polynomials. 2.9. Summary. 2.10. Exercises. 2.11. Notes and sources -- 3. Moments. 3.1. The one-dimensional moment problem. 3.2. The multi-dimensional moment problem. 3.3. The K-moment problem. 3.4. Moment conditions for bounded density. 3.5. Summary. 3.6. Exercises. 3.7. Notes and sources -- 4. Algorithms for moment problems. 4.1. The overall approach. 4.2. Semidefinite relaxations. 4.3. Extraction of solutions. 4.4. Linear relaxations. 4.5. Extensions. 4.6. Exploiting sparsity. 4.7. Summary. 4.8. Exercises. 4.9. Notes and sources. 4.10. Proofs -- 5. Global optimization over polynomials. 5.1. The primal and dual perspectives. 5.2. Unconstrained polynomial optimization. 5.3. Constrained polynomial optimization : semidefinite relaxations. 5.4. Linear programming relaxations. 5.5. Global optimality conditions. 5.6. Convex polynomial programs. 5.7. Discrete optimization. 5.8. Global minimization of a rational function. 5.9. Exploiting symmetry. 5.10. Summary. 5.11. Exercises. 5.12. Notes and sources -- 6. Systems of polynomial equations. 6.1. Introduction. 6.2. Finding a real solution to systems of polynomial equations. 6.3. Finding all complex and/or all real solutions : a unified treatment. 6.4. Summary. 6.5. Exercises. 6.6. Notes and sources -- 7. Applications in probability. 7.1. Upper bounds on measures with moment conditions. 7.2. Measuring basic semi-algebraic sets. 7.3. Measures with given marginals. 7.4. Summary. 7.5. Exercises. 7.6. Notes and sources -- 8. Markov chains applications. 8.1. Bounds on invariant measures. 8.2. Evaluation of ergodic criteria. 8.3. Summary. 8.4. Exercises. 8.5. Notes and sources -- 9. Application in mathematical finance. 9.1. Option pricing with moment information. 9.2. Option pricing with a dynamic model. 9.3. Summary. 9.4. Notes and sources -- 10. Application in control. 10.1. Introduction. 10.2. Weak formulation of optimal control problems. 10.3. Semidefinite relaxations for the OCP. 10.4. Summary. 10.5. Notes and sources -- 11. Convex envelope and representation of convex sets. 11.1. The convex envelope of a rational function. 11.2. Semidefinite representation of convex sets. 11.3. Algebraic certificates of convexity. 11.4. Summary. 11.5. Exercises. 11.6. Notes and sources -- 12. Multivariate integration 12.1. Integration of a rational function. 12.2. Integration of exponentials of polynomials. 12.3. Maximum entropy estimation. 12.4. Summary. 12.5. Exercises. 12.6. Notes and sources -- 13. Min-max problems and Nash equilibria. 13.1. Robust polynomial optimization. 13.2. Minimizing the sup of finitely many rational cunctions. 13.3. Application to Nash equilibria. 13.4. Exercises. 13.5. Notes and sources -- 14. Bounds on linear PDE. 14.1. Linear partial differential equations. 14.2. Notes and sources
Author: J. A. Shohat
Publisher:
ISBN:
Category :
Languages : en
Pages : 144
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Book Description
Author: James Shohat
Publisher:
ISBN:
Category : Continued fractions
Languages : en
Pages : 144
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Book Description
Author: James Alexander Shohat
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: James Alexander Shohat
Publisher:
ISBN:
Category :
Languages : en
Pages : 144
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Book Description
Author: Chip Heath
Publisher: Simon and Schuster
ISBN: 1501147765
Category : Business & Economics
Languages : en
Pages : 320
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Book Description
The New York Times bestselling authors of Switch and Made to Stick explore why certain brief experiences can jolt us and elevate us and change us—and how we can learn to create such extraordinary moments in our life and work. While human lives are endlessly variable, our most memorable positive moments are dominated by four elements: elevation, insight, pride, and connection. If we embrace these elements, we can conjure more moments that matter. What if a teacher could design a lesson that he knew his students would remember twenty years later? What if a manager knew how to create an experience that would delight customers? What if you had a better sense of how to create memories that matter for your children? This book delves into some fascinating mysteries of experience: Why we tend to remember the best or worst moment of an experience, as well as the last moment, and forget the rest. Why “we feel most comfortable when things are certain, but we feel most alive when they’re not.” And why our most cherished memories are clustered into a brief period during our youth. Readers discover how brief experiences can change lives, such as the experiment in which two strangers meet in a room, and forty-five minutes later, they leave as best friends. (What happens in that time?) Or the tale of the world’s youngest female billionaire, who credits her resilience to something her father asked the family at the dinner table. (What was that simple question?) Many of the defining moments in our lives are the result of accident or luck—but why would we leave our most meaningful, memorable moments to chance when we can create them? The Power of Moments shows us how to be the author of richer experiences.
Author: Hubert Stanley Wall
Publisher: Courier Dover Publications
ISBN: 0486830446
Category : Mathematics
Languages : en
Pages : 449
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Book Description
One of the most authoritative and comprehensive books on the subject of continued fractions, this monograph has been widely used by generations of mathematicians and their students. Dr. Hubert Stanley Wall presents a unified theory correlating certain parts and applications of the subject within a larger analytic structure. Prerequisites include a first course in function theory and knowledge of the elementary properties of linear transformations in the complex plane. Some background in number theory, real analysis, and complex analysis may also prove helpful. The two-part treatment begins with an exploration of convergence theory, addressing continued fractions as products of linear fractional transformations, convergence theorems, and the theory of positive definite continued fractions, as well as other topics. The second part, focusing on function theory, covers the theory of equations, matrix theory of continued fractions, bounded analytic functions, and many additional subjects.
