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Subharmonic Functions

Author: Walter Kurt Hayman
Publisher: Academic Pr
Size: 17.79 MB
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Building on the foundation laid in the first volume of Subharmonic Functions, which has become a classic, this second volume deals extensively with applications to functions of a complex variable. The material also has applications in differential equations and differential equations and differential geometry. It reflects the increasingly important role that subharmonic functions play in these areas of mathematics. The presentation goes back to the pioneering work of Ahlfors, Heins, and Kjellberg, leading to and including the more recent results of Baernstein, Weitsman, and many others. The volume also includes some previously unpublished material. It addresses mathematicians from graduate students to researchers in the field and will also appeal to physicists and electrical engineers who use these tools in their research work. The extensive preface and introductions to each chapter give readers an overview. A series of examples helps readers test their understatnding of the theory and the master the applications.

Symmetrization In Analysis

Author: Albert Baernstein II
Publisher: Cambridge University Press
ISBN: 0521830478
Size: 53.75 MB
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Develops the modern theory of symmetrization including applications to geometry, PDEs, and real and complex analysis.

Potential Theory In The Complex Plane

Author: Thomas Ransford
Publisher: Cambridge University Press
ISBN: 9780521466547
Size: 13.67 MB
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Ransford provides an introduction to the subject, concentrating on the important case of two dimensions, and emphasizing its links with complex analysis. This is reflected in the large number of applications, which include Picard's theorem, the Phragmén-Lindelöf principle, the Radó-Stout theorem, Lindelöf's theory of asymptotic values, the Riemann mapping theorem (including continuity at the boundary), the Koebe one-quarter theorem, Hilbert's lemniscate theorem, and the sharp quantitative form of Runge's theorem. In addition, there is a chapter on connections with functional analysis and dynamical systems, which shows how the theory can be applied to other parts of mathematics and gives a flavor of some recent research in the area.

Selected Papers On Differential Equations And Analysis

Publisher: American Mathematical Soc.
ISBN: 9780821839270
Size: 20.61 MB
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This volume contains translations of papers that originally appeared in the Japanese journal ""Sugaku"". The papers range over a variety of topics, including differential equations with free boundary, singular integral operators, operator algebras, and relations between the Brownian motion on a manifold with function theory. The volume is suitable for graduate students and research mathematicians interested in analysis and differential equations.

Nonlinear Potential Theory Of Degenerate Elliptic Equations

Author: Juha Heinonen
Publisher: Courier Dover Publications
ISBN: 0486830462
Size: 10.37 MB
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A self-contained treatment appropriate for advanced undergraduates and graduate students, this text offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. 1993 edition.

Pluripotential Theory

Author: Maciej Klimek
Publisher: Oxford University Press on Demand
Size: 73.19 MB
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Pluripotential theory is a recently developed non-linear complex counterpart of classical potential theory. Its main area of application is multidimensional complex analysis. The central part of the pluripotential theory is occupied by maximal plurisubharmonic functions and the generalized complex Monge-Ampere operator. The interplay between these two concepts provides the focal point of this monograph, which contains an up-to-date account of the developments from the large volume of recent work in this area. A substantial proportion of the work is devoted to classical properties of subharmonic and plurisubharmonic functions, which makes the pluripotential theory available for the first time to a wide audience of analysts.