Foundations Of Modern Potential Theory
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Foundations Of Modern Potential Theory
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Author : Naum Samoĭlovich Landkof
language : en
Publisher: Springer
Release Date : 1972
Foundations Of Modern Potential Theory written by Naum Samoĭlovich Landkof 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.
Foundations Of Modern Potential Theory
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Author : N. S. Landkof
language : de
Publisher:
Release Date : 1972
Foundations Of Modern Potential Theory written by N. S. Landkof and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with categories.
Potential Theory Selected Topics
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Author : Hiroaki Aikawa
language : en
Publisher: Springer
Release Date : 2006-11-14
Potential Theory Selected Topics written by Hiroaki Aikawa and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The first part of these lecture notes is an introduction to potential theory to prepare the reader for later parts, which can be used as the basis for a series of advanced lectures/seminars on potential theory/harmonic analysis. Topics covered in the book include minimal thinness, quasiadditivity of capacity, applications of singular integrals to potential theory, L(p)-capacity theory, fine limits of the Nagel-Stein boundary limit theorem and integrability of superharmonic functions. The notes are written for an audience familiar with the theory of integration, distributions and basic functional analysis.
Potential Theory
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Author : Jürgen Bliedtner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Potential Theory written by Jürgen Bliedtner 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.
During the last thirty years potential theory has undergone a rapid development, much of which can still only be found in the original papers. This book deals with one part of this development, and has two aims. The first is to give a comprehensive account of the close connection between analytic and probabilistic potential theory with the notion of a balayage space appearing as a natural link. The second aim is to demonstrate the fundamental importance of this concept by using it to give a straight presentation of balayage theory which in turn is then applied to the Dirichlet problem. We have considered it to be beyond the scope of this book to treat further topics such as duality, ideal boundary and integral representation, energy and Dirichlet forms. The subject matter of this book originates in the relation between classical potential theory and the theory of Brownian motion. Both theories are linked with the Laplace operator. However, the deep connection between these two theories was first revealed in the papers of S. KAKUTANI [1], [2], [3], M. KAC [1] and J. L. DO DB [2] during the period 1944-54: This can be expressed by the·fact that the harmonic measures which occur in the solution of the Dirichlet problem are hitting distri butions for Brownian motion or, equivalently, that the positive hyperharmonic func tions for the Laplace equation are the excessive functions of the Brownian semi group.
Classical Potential Theory
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Author : David H. Armitage
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Classical Potential Theory written by David H. Armitage 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.
From its origins in Newtonian physics, potential theory has developed into a major field of mathematical research. This book provides a comprehensive treatment of classical potential theory: it covers harmonic and subharmonic functions, maximum principles, polynomial expansions, Green functions, potentials and capacity, the Dirichlet problem and boundary integral representations. The first six chapters deal concretely with the basic theory, and include exercises. The final three chapters are more advanced and treat topological ideas specifically created for potential theory, such as the fine topology, the Martin boundary and minimal thinness. The presentation is largely self-contained and is accessible to graduate students, the only prerequisites being a reasonable grounding in analysis and several variables calculus, and a first course in measure theory. The book will prove an essential reference to all those with an interest in potential theory and its applications.
Potential Theory
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Author : Lester Helms
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-27
Potential Theory written by Lester Helms 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 2009-05-27 with Mathematics categories.
The ?rst six chapters of this book are revised versions of the same chapters in the author’s 1969 book, Introduction to Potential Theory. Atthetimeof the writing of that book, I had access to excellent articles,books, and lecture notes by M. Brelot. The clarity of these works made the task of collating them into a single body much easier. Unfortunately, there is not a similar collection relevant to more recent developments in potential theory. A n- comer to the subject will ?nd the journal literature to be a maze of excellent papers and papers that never should have been published as presented. In the Opinion Column of the August, 2008, issue of the Notices of the Am- ican Mathematical Society, M. Nathanson of Lehman College (CUNY) and (CUNY) Graduate Center said it best “. . . When I read a journal article, I often ?nd mistakes. Whether I can ?x them is irrelevant. The literature is unreliable. ” From time to time, someone must try to ?nd a path through the maze. In planning this book, it became apparent that a de?ciency in the 1969 book would have to be corrected to include a discussion of the Neumann problem, not only in preparation for a discussion of the oblique derivative boundary value problem but also to improve the basic part of the subject matter for the end users, engineers, physicists, etc.
Potential Theory
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Author : Masanori Kishi
language : en
Publisher: Walter de Gruyter
Release Date : 2011-05-02
Potential Theory written by Masanori Kishi 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 2011-05-02 with Mathematics categories.
No detailed description available for "Potential Theory".
Potential Theory In The Complex Plane
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Author : Thomas Ransford
language : en
Publisher: Cambridge University Press
Release Date : 1995-03-16
Potential Theory In The Complex Plane written by Thomas Ransford and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-03-16 with Mathematics categories.
Potential theory is the broad area of mathematical analysis encompassing such topics as harmonic and subharmonic functions.
Classical Potential Theory And Its Probabilistic Counterpart
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Author : Joseph L. Doob
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Classical Potential Theory And Its Probabilistic Counterpart written by Joseph L. Doob 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.
From the reviews: "This huge book written in several years by one of the few mathematicians able to do it, appears as a precise and impressive study (not very easy to read) of this bothsided question that replaces, in a coherent way, without being encyclopaedic, a large library of books and papers scattered without a uniform language. Instead of summarizing the author gives his own way of exposition with original complements. This requires no preliminary knowledge. ...The purpose which the author explains in his introduction, i.e. a deep probabilistic interpretation of potential theory and a link between two great theories, appears fulfilled in a masterly manner". M. Brelot in Metrika (1986)
Stratified Lie Groups And Potential Theory For Their Sub Laplacians
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Author : Andrea Bonfiglioli
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-24
Stratified Lie Groups And Potential Theory For Their Sub Laplacians written by Andrea Bonfiglioli 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 2007-08-24 with Mathematics categories.
This book provides an extensive treatment of Potential Theory for sub-Laplacians on stratified Lie groups. It also provides a largely self-contained presentation of stratified Lie groups, and of their Lie algebra of left-invariant vector fields. The presentation is accessible to graduate students and requires no specialized knowledge in algebra or differential geometry.