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Author : Hiroaki Aikawa,Matts Essen
Publisher : Unknown
Page : 216 pages
File Size : 47,8 Mb
Release : 2014-09-01
Category : Electronic
ISBN : 3662184427
Author : Hiroaki Aikawa,Matts Essen
Publisher : Springer
Page : 208 pages
File Size : 50,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540699910
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 : John Wermer
Publisher : Springer Science & Business Media
Page : 156 pages
File Size : 42,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662127278
Potential theory grew out of mathematical physics, in particular out of the theory of gravitation and the theory of electrostatics. Mathematical physicists such as Poisson and Green introduced some of the central ideas of the subject. A mathematician with a general knowledge of analysis may find it useful to begin his study of classical potential theory by looking at its physical origins. Sections 2, 5 and 6 of these Notes give in part heuristic arguments based on physical considerations. These heuristic arguments suggest mathematical theorems and provide the mathematician with the problem of finding the proper hypotheses and mathematical proofs. These Notes are based on a one-semester course given by the author at Brown University in 1971. On the part of the reader, they assume a knowledge of Real Function Theory to the extent of a first year graduate course. In addition some elementary facts regarding harmonic functions are aS$umed as known. For convenience we have listed these facts in the Appendix. Some notation is also explained there. Essentially all the proofs we give in the Notes are for Euclidean 3-space R3 and Newtonian potentials ~.
Author : Juha Heinonen,Tero Kipelainen,Olli Martio
Publisher : Courier Dover Publications
Page : 417 pages
File Size : 42,6 Mb
Release : 2018-05-16
Category : Mathematics
ISBN : 9780486824253
A self-contained treatment appropriate for advanced undergraduate and graduate students, this volume offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. Starting with the theory of weighted Sobolev spaces, the text advances to the theory of weighted variational capacity. Succeeding chapters investigate solutions and supersolutions of equations, with emphasis on refined Sobolev spaces, variational integrals, and harmonic functions. Chapter 7 defines superharmonic functions via the comparison principle, and chapters 8 through 14 form the core of the nonlinear potential theory of superharmonic functions. Topics include balayage; Perron's method, barriers, and resolutivity; polar sets; harmonic measure; fine topology; harmonic morphisms; and quasiregular mappings. The book concludes with explorations of axiomatic nonlinear potential theory and helpful appendixes.
Author : Pandelis Dodos
Publisher : Springer
Page : 168 pages
File Size : 46,9 Mb
Release : 2010-04-15
Category : Mathematics
ISBN : 9783642121531
These notes are devoted to the study of some classical problems in the Geometry of Banach spaces. The novelty lies in the fact that their solution relies heavily on techniques coming from Descriptive Set Theory. Thecentralthemeisuniversalityproblems.Inparticular,thetextprovides an exposition of the methods developed recently in order to treat questions of the following type: (Q) LetC be a class of separable Banach spaces such that every space X in the classC has a certain property, say property (P). When can we ?nd a separable Banach space Y which has property (P) and contains an isomorphic copy of every member ofC? We will consider quite classical properties of Banach spaces, such as “- ing re?exive,” “having separable dual,” “not containing an isomorphic copy of c ,” “being non-universal,” etc. 0 It turns out that a positive answer to problem (Q), for any of the above mentioned properties, is possible if (and essentially only if) the classC is “simple.” The “simplicity” ofC is measured in set theoretic terms. Precisely, if the classC is analytic in a natural “coding” of separable Banach spaces, then we can indeed ?nd a separable space Y which is universal for the class C and satis?es the requirements imposed above.
Author : Andre Boivin,Javad Mashreghi
Publisher : American Mathematical Soc.
Page : 347 pages
File Size : 55,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821891735
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.
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 54,5 Mb
Release : 1988
Category : Electronic
ISBN : OCLC:916080994
Author : Richard J. Blakely
Publisher : Cambridge University Press
Page : 468 pages
File Size : 46,9 Mb
Release : 1996-09-13
Category : Mathematics
ISBN : 0521575478
This text bridges the gap between the classic texts on potential theory and modern books on applied geophysics. It opens with an introduction to potential theory, emphasising those aspects particularly important to earth scientists, such as Laplace's equation, Newtonian potential, magnetic and electrostatic fields, and conduction of heat. The theory is then applied to the interpretation of gravity and magnetic anomalies, drawing on examples from modern geophysical literature. Topics explored include regional and global fields, forward modeling, inverse methods, depth-to-source estimation, ideal bodies, analytical continuation, and spectral analysis. The book includes numerous exercises and a variety of computer subroutines written in FORTRAN. Graduate students and researchers in geophysics will find this book essential.
Author : Andrea Bonfiglioli,Ermanno Lanconelli,Francesco Uguzzoni
Publisher : Springer Science & Business Media
Page : 812 pages
File Size : 55,7 Mb
Release : 2007-08-24
Category : Mathematics
ISBN : 9783540718970
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.
Author : David H. Armitage,Stephen J. Gardiner
Publisher : Springer Science & Business Media
Page : 343 pages
File Size : 54,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447102335
A long-awaited, updated introductory text by the world leaders in potential theory. This essential reference work covers all aspects of this major field of mathematical research, from basic theory and exercises to more advanced topological ideas. The largely self-contained presentation makes it basically accessible to graduate students.
Author : Thomas Ransford
Publisher : Cambridge University Press
Page : 246 pages
File Size : 53,5 Mb
Release : 1995-03-16
Category : Mathematics
ISBN : 0521466547
Potential theory is the broad area of mathematical analysis encompassing such topics as harmonic and subharmonic functions.
Author : Oliver Dimon Kellogg
Publisher : Courier Corporation
Page : 404 pages
File Size : 48,6 Mb
Release : 1953-01-01
Category : Science
ISBN : 0486601447
Introduction to fundamentals of potential functions covers the force of gravity, fields of force, potentials, harmonic functions, electric images and Green's function, sequences of harmonic functions, fundamental existence theorems, the logarithmic potential, and much more. Detailed proofs rigorously worked out. 1929 edition.
Author : Juha Heinonen,Pekka Koskela,Nageswari Shanmugalingam,Jeremy T. Tyson
Publisher : Cambridge University Press
Page : 447 pages
File Size : 47,6 Mb
Release : 2015-02-05
Category : Mathematics
ISBN : 9781107092341
This coherent treatment from first principles is an ideal introduction for graduate students and a useful reference for experts.
Author : J. Coates,R. Greenberg,K.A. Ribet,K. Rubin
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 43,8 Mb
Release : 1999-10-19
Category : Mathematics
ISBN : 3540665463
This volume contains the expanded versions of the lectures given by the authors at the C.I.M.E. instructional conference held in Cetraro, Italy, from July 12 to 19, 1997. The papers collected here are broad surveys of the current research in the arithmetic of elliptic curves, and also contain several new results which cannot be found elsewhere in the literature. Owing to clarity and elegance of exposition, and to the background material explicitly included in the text or quoted in the references, the volume is well suited to research students as well as to senior mathematicians.
Author : René L. Schilling,Lothar Partzsch
Publisher : Walter de Gruyter GmbH & Co KG
Page : 514 pages
File Size : 41,5 Mb
Release : 2014-08-22
Category : Mathematics
ISBN : 9783110373981
Brownian motion is one of the most important stochastic processes in continuous time and with continuous state space. Within the realm of stochastic processes, Brownian motion is at the intersection of Gaussian processes, martingales, Markov processes, diffusions and random fractals, and it has influenced the study of these topics. Its central position within mathematics is matched by numerous applications in science, engineering and mathematical finance. Often textbooks on probability theory cover, if at all, Brownian motion only briefly. On the other hand, there is a considerable gap to more specialized texts on Brownian motion which is not so easy to overcome for the novice. The authors’ aim was to write a book which can be used as an introduction to Brownian motion and stochastic calculus, and as a first course in continuous-time and continuous-state Markov processes. They also wanted to have a text which would be both a readily accessible mathematical back-up for contemporary applications (such as mathematical finance) and a foundation to get easy access to advanced monographs. This textbook, tailored to the needs of graduate and advanced undergraduate students, covers Brownian motion, starting from its elementary properties, certain distributional aspects, path properties, and leading to stochastic calculus based on Brownian motion. It also includes numerical recipes for the simulation of Brownian motion.