Minimal Positive Harmonic Functions PDF Download
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Author: Pieter Johannes Kostense
Publisher:
ISBN:
Category :
Languages : en
Pages : 72
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Book Description
Author: Pieter Johannes Kostense
Publisher:
ISBN:
Category :
Languages : en
Pages : 72
Get Book Here
Book Description
Author: Ross G. Pinsky
Publisher: Cambridge University Press
ISBN: 0521470145
Category : Mathematics
Languages : en
Pages : 492
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Book Description
In this book, Professor Pinsky gives a self-contained account of the theory of positive harmonic functions for second order elliptic operators, using an integrated probabilistic and analytic approach. The book begins with a treatment of the construction and basic properties of diffusion processes. This theory then serves as a vehicle for studying positive harmonic funtions. Starting with a rigorous treatment of the spectral theory of elliptic operators with nice coefficients on smooth, bounded domains, the author then develops the theory of the generalized principal eigenvalue, and the related criticality theory for elliptic operators on arbitrary domains. Martin boundary theory is considered, and the Martin boundary is explicitly calculated for several classes of operators. The book provides an array of criteria for determining whether a diffusion process is transient or recurrent. Also introduced are the theory of bounded harmonic functions, and Brownian motion on manifolds of negative curvature. Many results that form the folklore of the subject are here given a rigorous exposition, making this book a useful reference for the specialist, and an excellent guide for the graduate student.
Author: J. L. Doob
Publisher: Springer Science & Business Media
ISBN: 1461252083
Category : Mathematics
Languages : en
Pages : 865
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Book Description
Potential theory and certain aspects of probability theory are intimately related, perhaps most obviously in that the transition function determining a Markov process can be used to define the Green function of a potential theory. Thus it is possible to define and develop many potential theoretic concepts probabilistically, a procedure potential theorists observe withjaun diced eyes in view of the fact that now as in the past their subject provides the motivation for much of Markov process theory. However that may be it is clear that certain concepts in potential theory correspond closely to concepts in probability theory, specifically to concepts in martingale theory. For example, superharmonic functions correspond to supermartingales. More specifically: the Fatou type boundary limit theorems in potential theory correspond to supermartingale convergence theorems; the limit properties of monotone sequences of superharmonic functions correspond surprisingly closely to limit properties of monotone sequences of super martingales; certain positive superharmonic functions [supermartingales] are called "potentials," have associated measures in their respective theories and are subject to domination principles (inequalities) involving the supports of those measures; in each theory there is a reduction operation whose properties are the same in the two theories and these reductions induce sweeping (balayage) of the measures associated with potentials, and so on.
Author: Josef Kral
Publisher: Walter de Gruyter
ISBN: 3110818574
Category : Mathematics
Languages : en
Pages : 513
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Book Description
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Author: Björn Gustafsson
Publisher: Springer Science & Business Media
ISBN: 3764399066
Category : Mathematics
Languages : en
Pages : 513
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Book Description
Our knowledge of objects of complex and potential analysis has been enhanced recently by ideas and constructions of theoretical and mathematical physics, such as quantum field theory, nonlinear hydrodynamics, material science. These are some of the themes of this refereed collection of papers, which grew out of the first conference of the European Science Foundation Networking Programme 'Harmonic and Complex Analysis and Applications' held in Norway 2007.
Author: M. Hazewinkel
Publisher: Springer
ISBN: 1489937935
Category : Mathematics
Languages : en
Pages : 952
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Book Description
Author: Hiroaki Aikawa
Publisher: Springer
ISBN: 3540699910
Category : Mathematics
Languages : en
Pages : 208
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Book Description
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.
Author: Guido Weiss
Publisher: American Mathematical Soc.
ISBN: 0821814362
Category : Generalized spaces
Languages : en
Pages : 488
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Book Description
Author: Philippe Biane
Publisher: Springer Science & Business Media
ISBN: 3540693645
Category : Mathematics
Languages : en
Pages : 467
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Book Description
This book offers the revised and completed notes of lectures given at the 2007 conference, "Quantum Potential Theory: Structures and Applications to Physics." These lectures provide an introduction to the theory and discuss various applications.
Author: Victor Anandam
Publisher: Springer Science & Business Media
ISBN: 3642213995
Category : Mathematics
Languages : en
Pages : 152
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Book Description
Random walks, Markov chains and electrical networks serve as an introduction to the study of real-valued functions on finite or infinite graphs, with appropriate interpretations using probability theory and current-voltage laws. The relation between this type of function theory and the (Newton) potential theory on the Euclidean spaces is well-established. The latter theory has been variously generalized, one example being the axiomatic potential theory on locally compact spaces developed by Brelot, with later ramifications from Bauer, Constantinescu and Cornea. A network is a graph with edge-weights that need not be symmetric. This book presents an autonomous theory of harmonic functions and potentials defined on a finite or infinite network, on the lines of axiomatic potential theory. Random walks and electrical networks are important sources for the advancement of the theory.
