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Author: Gustave Choquet
Publisher:
ISBN:
Category : Functions
Languages : en
Pages : 192
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Book Description
Author: Gustave Choquet
Publisher:
ISBN:
Category : Functions
Languages : en
Pages : 192
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Book Description
Author: Gustave Choquet
Publisher:
ISBN:
Category :
Languages : en
Pages : 179
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Book Description
Author: Gustave Choquet
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Xavier Tolsa
Publisher: Springer Science & Business Media
ISBN: 3319005960
Category : Mathematics
Languages : en
Pages : 402
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Book Description
This book studies some of the groundbreaking advances that have been made regarding analytic capacity and its relationship to rectifiability in the decade 1995–2005. The Cauchy transform plays a fundamental role in this area and is accordingly one of the main subjects covered. Another important topic, which may be of independent interest for many analysts, is the so-called non-homogeneous Calderón-Zygmund theory, the development of which has been largely motivated by the problems arising in connection with analytic capacity. The Painlevé problem, which was first posed around 1900, consists in finding a description of the removable singularities for bounded analytic functions in metric and geometric terms. Analytic capacity is a key tool in the study of this problem. In the 1960s Vitushkin conjectured that the removable sets which have finite length coincide with those which are purely unrectifiable. Moreover, because of the applications to the theory of uniform rational approximation, he posed the question as to whether analytic capacity is semiadditive. This work presents full proofs of Vitushkin’s conjecture and of the semiadditivity of analytic capacity, both of which remained open problems until very recently. Other related questions are also discussed, such as the relationship between rectifiability and the existence of principal values for the Cauchy transforms and other singular integrals. The book is largely self-contained and should be accessible for graduate students in analysis, as well as a valuable resource for researchers.
Author: Christopher J. Preston
Publisher:
ISBN:
Category : Convergence
Languages : en
Pages : 132
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Author: Gustave Choquet (mathématicien).)
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Author: Vladimir N. Dubinin
Publisher: Springer
ISBN: 3034808437
Category : Science
Languages : en
Pages : 352
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Book Description
This is the first systematic presentation of the capacitory approach and symmetrization in the context of complex analysis. The content of the book is original – the main part has not been covered by existing textbooks and monographs. After an introduction to the theory of condenser capacities in the plane, the monotonicity of the capacity under various special transformations (polarization, Gonchar transformation, averaging transformations and others) is established, followed by various types of symmetrization which are one of the main objects of the book. By using symmetrization principles, some metric properties of compact sets are obtained and some extremal decomposition problems are solved. Moreover, the classical and present facts for univalent and multivalent meromorphic functions are proven. This book will be a valuable source for current and future researchers in various branches of complex analysis and potential theory.
Author: Michel Grabisch
Publisher: Springer
ISBN: 3319306901
Category : Mathematics
Languages : en
Pages : 482
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Book Description
The book provides a thorough treatment of set functions, games and capacities as well as integrals with respect to capacities and games, in a mathematical rigorous presentation and in view of application to decision making. After a short chapter introducing some required basic knowledge (linear programming, polyhedra, ordered sets) and notation, the first part of the book consists of three long chapters developing the mathematical aspects. This part is not related to a particular application field and, by its neutral mathematical style, is useful to the widest audience. It gathers many results and notions which are scattered in the literature of various domains (game theory, decision, combinatorial optimization and operations research). The second part consists of three chapters, applying the previous notions in decision making and modelling: decision under uncertainty, decision with multiple criteria, possibility theory and Dempster-Shafer theory.
Author: Deborah Eade
Publisher: Oxfam
ISBN: 9780855983666
Category : Social Science
Languages : en
Pages : 236
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Book Description
This book considers specific and practical ways in which NGO's can contribute to enabling people to build on the capacities they already possess. It reviews the types of social organisation with which NGO's might consider working and the provision of training in a variety of relevant skills and activities.
Author: David R. Adams
Publisher: Springer Science & Business Media
ISBN: 3662032821
Category : Mathematics
Languages : en
Pages : 372
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Book Description
"..carefully and thoughtfully written and prepared with, in my opinion, just the right amount of detail included...will certainly be a primary source that I shall turn to." Proceedings of the Edinburgh Mathematical Society
