Function Spaces And Potential Theory
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Function Spaces And Potential Theory
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Author : David R. Adams
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Function Spaces And Potential Theory written by David R. Adams and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
"..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
Integral Representation Theory
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Author : Jaroslav Lukeš
language : en
Publisher: Walter de Gruyter
Release Date : 2010
Integral Representation Theory written by Jaroslav Lukeš and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
This monograph presents the state of the art of convexity, with an emphasis to integral representation. The exposition is focused on Choquet's theory of function spaces with a link to compact convex sets. An important feature of the book is an interplay between various mathematical subjects, such as functional analysis, measure theory, descriptive set theory, Banach spaces theory and potential theory. A substantial part of the material is of fairly recent origin and many results appear in the book form for the first time. The text is self-contained and covers a wide range of applications. From the contents: Geometry of convex sets Choquet theory of function spaces Affine functions on compact convex sets Perfect classes of functions and representation of affine functions Simplicial function spaces Choquet's theory of function cones Topologies on boundaries Several results on function spaces and compact convex sets Continuous and measurable selectors Construction of function spaces Function spaces in potential theory and Dirichlet problem Applications
Nonlinear Potential Theory On Metric Spaces
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Author : Anders Björn
language : en
Publisher: European Mathematical Society
Release Date : 2011
Nonlinear Potential Theory On Metric Spaces written by Anders Björn and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Harmonic functions categories.
The $p$-Laplace equation is the main prototype for nonlinear elliptic problems and forms a basis for various applications, such as injection moulding of plastics, nonlinear elasticity theory, and image processing. Its solutions, called p-harmonic functions, have been studied in various contexts since the 1960s, first on Euclidean spaces and later on Riemannian manifolds, graphs, and Heisenberg groups. Nonlinear potential theory of p-harmonic functions on metric spaces has been developing since the 1990s and generalizes and unites these earlier theories. This monograph gives a unified treatment of the subject and covers most of the available results in the field, so far scattered over a large number of research papers. The aim is to serve both as an introduction to the area for interested readers and as a reference text for active researchers. The presentation is rather self contained, but it is assumed that readers know measure theory and functional analysis. The first half of the book deals with Sobolev type spaces, so-called Newtonian spaces, based on upper gradients on general metric spaces. In the second half, these spaces are used to study p-harmonic functions on metric spaces, and a nonlinear potential theory is developed under some additional, but natural, assumptions on the underlying metric space. Each chapter contains historical notes with relevant references, and an extensive index is provided at the end of the book.
Studies In Potential Theory And Function Spaces
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Author : Torbjörn Kolsrud
language : en
Publisher:
Release Date : 1983
Studies In Potential Theory And Function Spaces written by Torbjörn Kolsrud and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with categories.
Theory Of Function Spaces
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Author : Hans Triebel
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-20
Theory Of Function Spaces written by Hans Triebel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-20 with Science categories.
The book deals with the two scales Bsp,q and Fsp,q of spaces of distributions, where ‐∞s∞ and 0p,q≤∞, which include many classical and modern spaces, such as Hölder spaces, Zygmund classes, Sobolev spaces, Besov spaces, Bessel-potential spaces, Hardy spaces and spaces of BMO-type. It is the main aim of this book to give a unified treatment of the corresponding spaces on the Euclidean n-space Rsubn
Nonlinear Potential Theory And Weighted Sobolev Spaces
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Author : Bengt O. Turesson
language : en
Publisher: Springer
Release Date : 2007-05-06
Nonlinear Potential Theory And Weighted Sobolev Spaces written by Bengt O. Turesson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-06 with Mathematics categories.
The book systematically develops the nonlinear potential theory connected with the weighted Sobolev spaces, where the weight usually belongs to Muckenhoupt's class of Ap weights. These spaces occur as solutions spaces for degenerate elliptic partial differential equations. The Sobolev space theory covers results concerning approximation, extension, and interpolation, Sobolev and Poincaré inequalities, Maz'ya type embedding theorems, and isoperimetric inequalities. In the chapter devoted to potential theory, several weighted capacities are investigated. Moreover, "Kellogg lemmas" are established for various concepts of thinness. Applications of potential theory to weighted Sobolev spaces include quasi continuity of Sobolev functions, Poincaré inequalities, and spectral synthesis theorems.
The Dirichlet Space And Related Function Spaces
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Author : Nicola Arcozzi
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-09-03
The Dirichlet Space And Related Function Spaces written by Nicola Arcozzi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-03 with Dirichlet principle categories.
The study of the classical Dirichlet space is one of the central topics on the intersection of the theory of holomorphic functions and functional analysis. It was introduced about100 years ago and continues to be an area of active current research. The theory is related to such important themes as multipliers, reproducing kernels, and Besov spaces, among others. The authors present the theory of the Dirichlet space and related spaces starting with classical results and including some quite recent achievements like Dirichlet-type spaces of functions in several complex variables and the corona problem. The first part of this book is an introduction to the function theory and operator theory of the classical Dirichlet space, a space of holomorphic functions on the unit disk defined by a smoothness criterion. The Dirichlet space is also a Hilbert space with a reproducing kernel, and is the model for the dyadic Dirichlet space, a sequence space defined on the dyadic tree. These various viewpoints are used to study a range of topics including the Pick property, multipliers, Carleson measures, boundary values, zero sets, interpolating sequences, the local Dirichlet integral, shift invariant subspaces, and Hankel forms. Recurring themes include analogies, sometimes weak and sometimes strong, with the classical Hardy space; and the analogy with the dyadic Dirichlet space. The final chapters of the book focus on Besov spaces of holomorphic functions on the complex unit ball, a class of Banach spaces generalizing the Dirichlet space. Additional techniques are developed to work with the nonisotropic complex geometry, including a useful invariant definition of local oscillation and a sophisticated variation on the dyadic Dirichlet space. Descriptions are obtained of multipliers, Carleson measures, interpolating sequences, and multiplier interpolating sequences; estimates are obtained to prove corona theorems.
Potential Theory On Harmonic Spaces
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Author : Corneliu Constantinescu
language : en
Publisher: Springer
Release Date : 1972
Potential Theory On Harmonic Spaces written by Corneliu Constantinescu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Mathematics categories.
There has been a considerable revival of interest in potential theory during the last 20 years. This is made evident by the appearance of new mathematical disciplines in that period which now-a-days are considered as parts of potential theory. Examples of such disciplines are: the theory of Choquet capacities, of Dirichlet spaces, of martingales and Markov processes, of integral representation in convex compact sets as well as the theory of harmonic spaces. All these theories have roots in classical potential theory. The theory of harmonic spaces, sometimes also called axiomatic theory of harmonic functions, plays a particular role among the above mentioned theories. On the one hand, this theory has particularly close connections with classical potential theory. Its main notion is that of a harmonic function and its main aim is the generalization and unification of classical results and methods for application to an extended class of elliptic and parabolic second order partial differential equations. On the other hand, the theory of harmonic spaces is closely related to the theory of Markov processes. In fact, all important notions and results of the theory have a probabilistic interpretation.
Complex Analysis And Potential Theory
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Author : Andre Boivin
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Complex Analysis And Potential Theory written by Andre Boivin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
This is the proceedings volume of an international conference entitled Complex Analysis and Potential Theory, which was held to honor the important contributions of two influential analysts, Kohur N. GowriSankaran and Paul M. Gauthier, in June 2011 at the Centre de Recherches Mathematiques (CRM) in Montreal. More than fifty mathematicians from fifteen countries participated in the conference. The twenty-four surveys and research articles contained in this book are based on the lectures given by some of the most established specialists in the fields. They reflect the wide breadth of research interests of the two honorees: from potential theory on trees to approximation on Riemann surfaces, from universality to inner and outer functions and the disc algebra, from branching processes to harmonic extension and capacities, from harmonic mappings and the Harnack principle to integration formulae in $\mathbb {C}^n$ and the Hartogs phenomenon, from fine harmonicity and plurisubharmonic functions to the binomial identity and the Riemann hypothesis, and more. This volume will be a valuable resource for specialists, young researchers, and graduate students from both fields, complex analysis and potential theory. It will foster further cooperation and the exchange of ideas and techniques to find new research perspectives.
Application Of The Theory Of Linear Operators In Hilbert Space To Potential Theory
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Author : E. J. Specht
language : en
Publisher:
Release Date : 1957
Application Of The Theory Of Linear Operators In Hilbert Space To Potential Theory written by E. J. Specht and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1957 with Hilbert space categories.