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Título : Derivatives of Inner Functions Tipo de documento: documento electrónico Autores: Javad Mashreghi ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Fields Institute Monographs, ISSN 10695273 num. 31 Número de páginas: X, 170 p Il.: online resource ISBN/ISSN/DL: 9781461456117 Idioma : Inglés (eng) Palabras clave: Mathematics Functional analysis Functions of complex variables a Complex Variable Analysis Several Variables and Analytic Spaces Clasificación: 51 Matemáticas Resumen: Derivatives of Inner Functions was inspired by a conference held at the Fields Institute in 2011 entitled "Blaschke Products and Their Applications." Inner functions form an important subclass of bounded analytic functions. Since they have unimodular boundary values, they appear in many extremal problems of complex analysis. They have been extensively studied since the early twentieth century and the literature on this topic is vast. This book is devoted to a concise study of derivatives of inner functions and is confined to treating the integral means of derivatives and presenting a comprehensive list of results on Hardy and Bergman means. This selfcontained monograph allows researchers to get acquainted with the essentials of inner functions, rendering this theory accessible to graduate students while providing the reader with rapid access to the frontiers of research in this field En línea: http://dx.doi.org/10.1007/9781461456117 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32263 Derivatives of Inner Functions [documento electrónico] / Javad Mashreghi ; SpringerLink (Online service) .  New York, NY : Springer New York : Imprint: Springer, 2013 .  X, 170 p : online resource.  (Fields Institute Monographs, ISSN 10695273; 31) .
ISBN : 9781461456117
Idioma : Inglés (eng)
Palabras clave: Mathematics Functional analysis Functions of complex variables a Complex Variable Analysis Several Variables and Analytic Spaces Clasificación: 51 Matemáticas Resumen: Derivatives of Inner Functions was inspired by a conference held at the Fields Institute in 2011 entitled "Blaschke Products and Their Applications." Inner functions form an important subclass of bounded analytic functions. Since they have unimodular boundary values, they appear in many extremal problems of complex analysis. They have been extensively studied since the early twentieth century and the literature on this topic is vast. This book is devoted to a concise study of derivatives of inner functions and is confined to treating the integral means of derivatives and presenting a comprehensive list of results on Hardy and Bergman means. This selfcontained monograph allows researchers to get acquainted with the essentials of inner functions, rendering this theory accessible to graduate students while providing the reader with rapid access to the frontiers of research in this field En línea: http://dx.doi.org/10.1007/9781461456117 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32263 Ejemplares
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Título : Lectures on Sphere Arrangements – the Discrete Geometric Side Tipo de documento: documento electrónico Autores: Károly Bezdek ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Fields Institute Monographs, ISSN 10695273 num. 32 Número de páginas: XII, 175 p Il.: online resource ISBN/ISSN/DL: 9781461481188 Idioma : Inglés (eng) Palabras clave: Mathematics Convex geometry Discrete Polytopes and Geometry Clasificación: 51 Matemáticas Resumen: This monograph gives a short introduction to parts of modern discrete geometry, in addition to leading the reader to the frontiers of geometric research on sphere arrangements. The readership is aimed at advanced undergraduate and early graduate students, as well as interested researchers. It contains 30 open research problems ideal for graduate students and researchers in mathematics and computer science. Additionally, this book may be considered ideal for a onesemester advanced undergraduate or graduate level course. The core of this book is based on three lectures given by the author at the Fields Institute during the thematic program on Discrete Geometry and Applications and contains four basic topics. The first two deal with active areas that have been outstanding from the birth of discrete geometry, namely dense sphere packings and tilings. Sphere packings and tilings have a very strong connection to number theory, coding, groups, and mathematical programming. Extending the tradition of studying packings of spheres is the investigation of the monotonicity of volume under contractions of arbitrary arrangements of spheres. The third major topic can be found under the sections on ballpolyhedra that study the possibility of extending the theory of convex polytopes to the family of intersections of congruent balls. This section of the text is connected in many ways to the abovementioned major topics as well as to some other important research areas such as that on coverings by planks (with close ties to geometric analysis). The fourth basic topic is discussed under covering balls by cylinders. Nota de contenido: 1. Unit Sphere Packings  2. Proofs on Unit Sphere Packings  3. Contractions of Sphere Arrangements  4. Proofs on Contractions of Sphere Arrangements  5. BallPolyhedra and Spindle Convex Bodies  6. Proofs on BallPolyhedra and Spindle Convex Bodies  7. Coverings by Cylinders  8. Proofs on Coverings by Cylinders  9. Research Problems  an Overview  Glossary  References En línea: http://dx.doi.org/10.1007/9781461481188 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32378 Lectures on Sphere Arrangements – the Discrete Geometric Side [documento electrónico] / Károly Bezdek ; SpringerLink (Online service) .  New York, NY : Springer New York : Imprint: Springer, 2013 .  XII, 175 p : online resource.  (Fields Institute Monographs, ISSN 10695273; 32) .
ISBN : 9781461481188
Idioma : Inglés (eng)
Palabras clave: Mathematics Convex geometry Discrete Polytopes and Geometry Clasificación: 51 Matemáticas Resumen: This monograph gives a short introduction to parts of modern discrete geometry, in addition to leading the reader to the frontiers of geometric research on sphere arrangements. The readership is aimed at advanced undergraduate and early graduate students, as well as interested researchers. It contains 30 open research problems ideal for graduate students and researchers in mathematics and computer science. Additionally, this book may be considered ideal for a onesemester advanced undergraduate or graduate level course. The core of this book is based on three lectures given by the author at the Fields Institute during the thematic program on Discrete Geometry and Applications and contains four basic topics. The first two deal with active areas that have been outstanding from the birth of discrete geometry, namely dense sphere packings and tilings. Sphere packings and tilings have a very strong connection to number theory, coding, groups, and mathematical programming. Extending the tradition of studying packings of spheres is the investigation of the monotonicity of volume under contractions of arbitrary arrangements of spheres. The third major topic can be found under the sections on ballpolyhedra that study the possibility of extending the theory of convex polytopes to the family of intersections of congruent balls. This section of the text is connected in many ways to the abovementioned major topics as well as to some other important research areas such as that on coverings by planks (with close ties to geometric analysis). The fourth basic topic is discussed under covering balls by cylinders. Nota de contenido: 1. Unit Sphere Packings  2. Proofs on Unit Sphere Packings  3. Contractions of Sphere Arrangements  4. Proofs on Contractions of Sphere Arrangements  5. BallPolyhedra and Spindle Convex Bodies  6. Proofs on BallPolyhedra and Spindle Convex Bodies  7. Coverings by Cylinders  8. Proofs on Coverings by Cylinders  9. Research Problems  an Overview  Glossary  References En línea: http://dx.doi.org/10.1007/9781461481188 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32378 Ejemplares
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Título : Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE Tipo de documento: documento electrónico Autores: Nizar Touzi ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Fields Institute Monographs, ISSN 10695273 num. 29 Número de páginas: X, 214 p Il.: online resource ISBN/ISSN/DL: 9781461442868 Idioma : Inglés (eng) Palabras clave: Mathematics Partial differential equations Economics, Mathematical Calculus of variations Probabilities Quantitative Finance Probability Theory and Stochastic Processes Differential Equations Variations Optimal Control; Optimization Clasificación: 51 Matemáticas Resumen: This book collects some recent developments in stochastic control theory with applications to financial mathematics. In the first part of the volume, standard stochastic control problems are addressed from the viewpoint of the recently developed weak dynamic programming principle. A special emphasis is put on regularity issues and, in particular, on the behavior of the value function near the boundary. Then a quick review of the main tools from viscosity solutions allowing one to overcome all regularity problems is provided. The second part is devoted to the class of stochastic target problems, which extends in a nontrivial way the standard stochastic control problems. Here the theory of viscosity solutions plays a crucial role in the derivation of the dynamic programming equation as the infinitesimal counterpart of the corresponding geometric dynamic programming equation. The various developments of this theory have been stimulated by applications in finance and by relevant connections with geometric flows; namely, the second order extension was motivated by illiquidity modeling, and the controlled loss version was introduced following the problem of quantile hedging. The third part presents an overview of backward stochastic differential equations and their extensions to the quadratic case. Backward stochastic differential equations are intimately related to the stochastic version of Pontryagin’s maximum principle and can be viewed as a strong version of stochastic target problems in the nonMarkov context. The main applications to the hedging problem under market imperfections, the optimal investment problem in the exponential or power expected utility framework, and some recent developments in the context of a Nash equilibrium model for interacting investors, are presented. The book concludes with a review of the numerical approximation techniques for nonlinear partial differential equations based on monotonic schemes methods in the theory of viscosity solutions Nota de contenido: Preface  1. Conditional Expectation and Linear Parabolic PDEs  2. Stochastic Control and Dynamic Programming  3. Optimal Stopping and Dynamic Programming  4. Solving Control Problems by Verification  5. Introduction to Viscosity Solutions  6. Dynamic Programming Equation in the Viscosity Sense  7. Stochastic Target Problems  8. Second Order Stochastic Target Problems  9. Backward SDEs and Stochastic Control  10. Quadratic Backward SDEs  11. Probabilistic Numerical Methods for Nonlinear PDEs  12. Introduction to Finite Differences Methods  References En línea: http://dx.doi.org/10.1007/9781461442868 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32217 Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE [documento electrónico] / Nizar Touzi ; SpringerLink (Online service) .  New York, NY : Springer New York : Imprint: Springer, 2013 .  X, 214 p : online resource.  (Fields Institute Monographs, ISSN 10695273; 29) .
ISBN : 9781461442868
Idioma : Inglés (eng)
Palabras clave: Mathematics Partial differential equations Economics, Mathematical Calculus of variations Probabilities Quantitative Finance Probability Theory and Stochastic Processes Differential Equations Variations Optimal Control; Optimization Clasificación: 51 Matemáticas Resumen: This book collects some recent developments in stochastic control theory with applications to financial mathematics. In the first part of the volume, standard stochastic control problems are addressed from the viewpoint of the recently developed weak dynamic programming principle. A special emphasis is put on regularity issues and, in particular, on the behavior of the value function near the boundary. Then a quick review of the main tools from viscosity solutions allowing one to overcome all regularity problems is provided. The second part is devoted to the class of stochastic target problems, which extends in a nontrivial way the standard stochastic control problems. Here the theory of viscosity solutions plays a crucial role in the derivation of the dynamic programming equation as the infinitesimal counterpart of the corresponding geometric dynamic programming equation. The various developments of this theory have been stimulated by applications in finance and by relevant connections with geometric flows; namely, the second order extension was motivated by illiquidity modeling, and the controlled loss version was introduced following the problem of quantile hedging. The third part presents an overview of backward stochastic differential equations and their extensions to the quadratic case. Backward stochastic differential equations are intimately related to the stochastic version of Pontryagin’s maximum principle and can be viewed as a strong version of stochastic target problems in the nonMarkov context. The main applications to the hedging problem under market imperfections, the optimal investment problem in the exponential or power expected utility framework, and some recent developments in the context of a Nash equilibrium model for interacting investors, are presented. The book concludes with a review of the numerical approximation techniques for nonlinear partial differential equations based on monotonic schemes methods in the theory of viscosity solutions Nota de contenido: Preface  1. Conditional Expectation and Linear Parabolic PDEs  2. Stochastic Control and Dynamic Programming  3. Optimal Stopping and Dynamic Programming  4. Solving Control Problems by Verification  5. Introduction to Viscosity Solutions  6. Dynamic Programming Equation in the Viscosity Sense  7. Stochastic Target Problems  8. Second Order Stochastic Target Problems  9. Backward SDEs and Stochastic Control  10. Quadratic Backward SDEs  11. Probabilistic Numerical Methods for Nonlinear PDEs  12. Introduction to Finite Differences Methods  References En línea: http://dx.doi.org/10.1007/9781461442868 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32217 Ejemplares
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Título : Uniform Spaces and Measures Tipo de documento: documento electrónico Autores: Jan Pachl ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Fields Institute Monographs, ISSN 10695273 num. 30 Número de páginas: X, 210 p Il.: online resource ISBN/ISSN/DL: 9781461450580 Idioma : Inglés (eng) Palabras clave: Mathematics Fourier analysis Functional Functions of complex variables Analysis a Complex Variable Clasificación: 51 Matemáticas Resumen: Uniform Spaces and Measures addresses the need for an accessible and comprehensive exposition of the theory of uniform measures  a need that became more critical when uniform measures recently reemerged in new results in abstract harmonic analysis. Until now, results about uniform measures have been scattered throughout many papers written by a number of authors, some unpublished, using a variety of definitions and notations. Uniform measures are functionals on the space of bounded uniformly continuous functions on a uniform space. They are a common generalization of several classes of measures and measurelike functionals studied in topological measure theory, probability theory, and abstract harmonic analysis. They offer a natural framework for results about topologies on spaces of measures and about the continuity of convolution of measures on topological groups and semitopological semigroups. This book can serve as a reference for the theory of uniform measures. It includes a selfcontained development of the theory with complete proofs, starting with the necessary parts of the theory of uniform spaces. It also includes several new results, and presents diverse results from many sources organized in a logical whole. The content is also suitable for graduate or advanced undergraduate courses on selected topics in topology and functional analysis, and contains a number of exercises with hints to solutions as well as several open problems with suggestions for further research Nota de contenido: Prerequisites  1. Uniformities and Topologies  2. Induced Uniform Structures  3. Uniform Structures on Semigroups  4. Some Notable Classes of Uniform Spaces  5. Measures on Complete Metric Spaces  6. Uniform Measures  7. Uniform Measures as Measures  8. Instances of Uniform Measures  9. Direct Product and Convolution  10. Free Uniform Measures  11. Approximation of Probability Distributions  12. Measurable Functionals  Hints to Excercises  References  Notation Index  Author Index  Subject Index En línea: http://dx.doi.org/10.1007/9781461450580 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32238 Uniform Spaces and Measures [documento electrónico] / Jan Pachl ; SpringerLink (Online service) .  New York, NY : Springer New York : Imprint: Springer, 2013 .  X, 210 p : online resource.  (Fields Institute Monographs, ISSN 10695273; 30) .
ISBN : 9781461450580
Idioma : Inglés (eng)
Palabras clave: Mathematics Fourier analysis Functional Functions of complex variables Analysis a Complex Variable Clasificación: 51 Matemáticas Resumen: Uniform Spaces and Measures addresses the need for an accessible and comprehensive exposition of the theory of uniform measures  a need that became more critical when uniform measures recently reemerged in new results in abstract harmonic analysis. Until now, results about uniform measures have been scattered throughout many papers written by a number of authors, some unpublished, using a variety of definitions and notations. Uniform measures are functionals on the space of bounded uniformly continuous functions on a uniform space. They are a common generalization of several classes of measures and measurelike functionals studied in topological measure theory, probability theory, and abstract harmonic analysis. They offer a natural framework for results about topologies on spaces of measures and about the continuity of convolution of measures on topological groups and semitopological semigroups. This book can serve as a reference for the theory of uniform measures. It includes a selfcontained development of the theory with complete proofs, starting with the necessary parts of the theory of uniform spaces. It also includes several new results, and presents diverse results from many sources organized in a logical whole. The content is also suitable for graduate or advanced undergraduate courses on selected topics in topology and functional analysis, and contains a number of exercises with hints to solutions as well as several open problems with suggestions for further research Nota de contenido: Prerequisites  1. Uniformities and Topologies  2. Induced Uniform Structures  3. Uniform Structures on Semigroups  4. Some Notable Classes of Uniform Spaces  5. Measures on Complete Metric Spaces  6. Uniform Measures  7. Uniform Measures as Measures  8. Instances of Uniform Measures  9. Direct Product and Convolution  10. Free Uniform Measures  11. Approximation of Probability Distributions  12. Measurable Functionals  Hints to Excercises  References  Notation Index  Author Index  Subject Index En línea: http://dx.doi.org/10.1007/9781461450580 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32238 Ejemplares
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