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| Author | : Corneliu Constantinescu |
| Publisher | : Springer |
| Total Pages | : 376 |
| Release | : 1972-12-05 |
| Genre | : Mathematics |
| ISBN | : |
Download Potential Theory on Harmonic Spaces Book in PDF, ePub and Kindle
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.
| Author | : Anders Björn |
| Publisher | : European Mathematical Society |
| Total Pages | : 422 |
| Release | : 2011 |
| Genre | : Harmonic functions |
| ISBN | : 9783037190999 |
Download Nonlinear Potential Theory on Metric Spaces Book in PDF, ePub and Kindle
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.
| Author | : M.A. Picardello |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 299 |
| Release | : 2013-11-11 |
| Genre | : Mathematics |
| ISBN | : 1489923233 |
Download Harmonic Analysis and Discrete Potential Theory Book in PDF, ePub and Kindle
This book collects the Proceedings of a Congress held in Frascati (Rome) in the period July 1 -July 10, 1991, on the subject of harmonic analysis and discrete potential theory, and related topics. The Congress was made possible by the financial support of the Italian National Research Council ("Gruppo GNAFA"), the Ministry of University ("Gruppo Analisi Funzionale" of the University of Milano), the University of Rome "Tor Vergata", and was also patronized by the Centro "Vito Volterra" of the University of Rome "Tor Vergata". Financial support for publishing these Proceedings was provided by the University of Rome "Tor Vergata", and by a generous contribution of the Centro "Vito Volterra". I am happy of this opportunity to acknowledge the generous support of all these Institutions, and to express my gratitude, and that of all the participants. A number of distinguished mathematicians took part in the Congress. Here is the list of participants: M. Babillot, F. Choucroun, Th. Coulhon, L. Elie, F. Ledrappier, N. Th. Varopoulos (Paris); L. Gallardo (Brest); Ph. Bougerol, B. Roynette (Nancy); O. Gebuhrer (Strasbourg); G. Ahumada-Bustamante (Mulhouse); A. Valette (Neuchatel); P. Gerl (Salzburg); W. Hansen, H. Leptin (Bielefeld); M. Bozejko, A. Hulanicki, T. Pytlik (Wroclaw); C. Thomassen (Lyngby); P. Sjogren (Goteborg); V. Kaimanovich (Leningrad); A. Nevo (Jerusalem); T. Steger (Chicago); S. Sawyer, M. Taibleson, G. Weiss (St. Louis); J. Cohen, S.S ali ani (Maryland); D. Voiculescu (Berkeley); A. Zemanian (Stony Brook); S. Northshield (Plattsburgh); J. Taylor (Montreal); J
| Author | : David R. Adams |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 372 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3662032821 |
Download Function Spaces and Potential Theory Book in PDF, ePub and Kindle
"..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
| Author | : Sheldon Axler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 266 |
| Release | : 2013-11-11 |
| Genre | : Mathematics |
| ISBN | : 1475781377 |
Download Harmonic Function Theory Book in PDF, ePub and Kindle
This book is about harmonic functions in Euclidean space. This new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bochers Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package supplements the text for readers who wish to explore harmonic function theory on a computer.
| Author | : Oliver Dimon Kellogg |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 395 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642867480 |
Download Foundations of Potential Theory Book in PDF, ePub and Kindle
The present volume gives a systematic treatment of potential functions. It takes its origin in two courses, one elementary and one advanced, which the author has given at intervals during the last ten years, and has a two-fold purpose: first, to serve as an introduction for students whose attainments in the Calculus include some knowledge of partial derivatives and multiple and line integrals; and secondly, to provide the reader with the fundamentals of the subject, so that he may proceed immediately to the applications, or to the periodical literature of the day. It is inherent in the nature of the subject that physical intuition and illustration be appealed to freely, and this has been done. However, that the book may present sound ideals to the student, and in order also serve the mathematician, both for purposes of reference and as a basis for further developments, the proofs have been given by rigorous methods. This has led, at a number of points, to results either not found elsewhere, or not readily accessible. Thus, Chapter IV contains a proof for the general regular region of the divergence theorem (Gauss', or Green's theorem) on the reduction of volume to surface integrals. The treatment of the fundamental existence theorems in Chapter XI by means of integral equations meets squarely the difficulties incident to ·the discontinuity of the kernel, and the same chapter gives an account of the most recent developments with respect to the Dirichlet problem.
| Author | : K. GowriSankaran |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 467 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401111383 |
Download Classical and Modern Potential Theory and Applications Book in PDF, ePub and Kindle
Proceedings of the NATO Advanced Research Workshop, Château de Bonas, France, July 25--31, 1993
| Author | : Corneliu Constantinescu |
| Publisher | : |
| Total Pages | : 354 |
| Release | : 1972 |
| Genre | : Harmonic functions |
| ISBN | : |
Download Potential Theory on Harmonic Spaces [by] Corneliu Constantinescu [and] Aurel Cornea Book in PDF, ePub and Kindle
| Author | : Victor Anandam |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 152 |
| Release | : 2011-06-27 |
| Genre | : Mathematics |
| ISBN | : 3642213995 |
Download Harmonic Functions and Potentials on Finite or Infinite Networks Book in PDF, ePub and Kindle
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.
| Author | : J. Wermer |
| Publisher | : Springer |
| Total Pages | : 173 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540384073 |
Download Potential Theory Book in PDF, ePub and Kindle
