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Author : George Swan
Publisher :
ISBN 13 :
Total Pages : 12 pages
Book Rating : 4.:/5 (83 download)
Download or read book For New Theorems in Harmonic Potential Theory written by George Swan and published by . This book was released on 1972 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : George W. Swan
Publisher :
ISBN 13 :
Total Pages : 12 pages
Book Rating : 4.:/5 (33 download)
Download or read book Three New Theorems in Harmonic Potential Theory written by George W. Swan and published by . This book was released on 1971 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : UNITED STATES. DEPARTMENT OF THE ARMY. MATHEMATICS RESEARCH CENTER.
Publisher :
ISBN 13 :
Total Pages : 39 pages
Book Rating : 4.:/5 (131 download)
Download or read book FOUR NEW THEOREMS IN HARMONIC POTENTIAL THEORY. MIXED BOUNDARY-VALUE PROBLEMS IN R WHEN IT IS GREATER THAN OR EQUAL TO 0, Z WHEN IT IS GREATER THAN OR EQUAL TO 0 written by UNITED STATES. DEPARTMENT OF THE ARMY. MATHEMATICS RESEARCH CENTER. and published by . This book was released on with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : John Wermer
Publisher : Springer Science & Business Media
ISBN 13 : 366212727X
Total Pages : 156 pages
Book Rating : 4.6/5 (621 download)
Download or read book Potential Theory written by John Wermer and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : George W. Swan
Publisher :
ISBN 13 :
Total Pages : 16 pages
Book Rating : 4.:/5 (227 download)
Download or read book Four New Theorems in Harmonic Potential Theory written by George W. Swan and published by . This book was released on 1972 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: Four new theorems are presented which enable one to obtain in a systematic manner the explicit solution to some mixed boundary-value problems in harmonic potential theory for the region r>or=0, z>or=0. These theorems obviate the necessity for solving dual integral equations. (Author).
Author : G. W. Swan
Publisher :
ISBN 13 :
Total Pages : 16 pages
Book Rating : 4.:/5 (227 download)
Download or read book Three New Theorems in Harmonic Potential Theory. Mixed Boundary-Value Problems in R Greater Than Or Equal to 0, Z Greater Than Or Equal to 0 written by G. W. Swan and published by . This book was released on 1971 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: Three new theorems are presented which state the form of solution to some mixed boundary-value problems in axially-symmetric harmonic potential theory for the region r> or = 0, z> or = 0. These theorems may provide a powerful tool for the solution of such problems and provide alternative methods for solving dual integral equations. Applications of the theory are discussed. (Author).
Author : Oliver Dimon Kellogg
Publisher : Springer Science & Business Media
ISBN 13 : 3642908500
Total Pages : 392 pages
Book Rating : 4.6/5 (429 download)
Download or read book Foundations of Potential Theory written by Oliver Dimon Kellogg and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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, in order that the book may present sound ideals to the student, and 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
ISBN 13 : 9401111383
Total Pages : 467 pages
Book Rating : 4.4/5 (11 download)
Download or read book Classical and Modern Potential Theory and Applications written by K. GowriSankaran and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Research Workshop, Château de Bonas, France, July 25--31, 1993
Author : Kellogg Oliver Dimon
Publisher : Barman Press
ISBN 13 : 1406706485
Total Pages : 396 pages
Book Rating : 4.4/5 (67 download)
Download or read book Foundations of Potential Theory written by Kellogg Oliver Dimon and published by Barman Press. This book was released on 2007-03-01 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.
Author : Thomas Ransford
Publisher : Cambridge University Press
ISBN 13 : 9780521466547
Total Pages : 246 pages
Book Rating : 4.4/5 (665 download)
Download or read book Potential Theory in the Complex Plane written by Thomas Ransford and published by Cambridge University Press. This book was released on 1995-03-16 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Potential theory is the broad area of mathematical analysis encompassing such topics as harmonic and subharmonic functions.
Author : Sheldon Axler
Publisher : Springer Science & Business Media
ISBN 13 : 1475781377
Total Pages : 266 pages
Book Rating : 4.4/5 (757 download)
Download or read book Harmonic Function Theory written by Sheldon Axler and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : M.A. Picardello
Publisher : Springer
ISBN 13 :
Total Pages : 320 pages
Book Rating : 4.:/5 (44 download)
Download or read book Harmonic Analysis and Discrete Potential Theory written by M.A. Picardello and published by Springer. This book was released on 1992-07-31 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : V. I. Fabrikant
Publisher : Dordrecht ; Boston : Kluwer Academic Publishers
ISBN 13 :
Total Pages : 492 pages
Book Rating : 4.:/5 (43 download)
Download or read book Applications of Potential Theory in Mechanics written by V. I. Fabrikant and published by Dordrecht ; Boston : Kluwer Academic Publishers. This book was released on 1989 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David H. Armitage
Publisher : Springer Science & Business Media
ISBN 13 : 1447102339
Total Pages : 343 pages
Book Rating : 4.4/5 (471 download)
Download or read book Classical Potential Theory written by David H. Armitage and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Victor Havin
Publisher : Springer Science & Business Media
ISBN 13 : 3642783775
Total Pages : 547 pages
Book Rating : 4.6/5 (427 download)
Download or read book The Uncertainty Principle in Harmonic Analysis written by Victor Havin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book is a collection of variations on a theme which can be summed up as follows: It is impossible for a non-zero function and its Fourier transform to be simultaneously very small. In other words, the approximate equalities x :::::: y and x :::::: fj cannot hold, at the same time and with a high degree of accuracy, unless the functions x and yare identical. Any information gained about x (in the form of a good approximation y) has to be paid for by a corresponding loss of control on x, and vice versa. Such is, roughly speaking, the import of the Uncertainty Principle (or UP for short) referred to in the title ofthis book. That principle has an unmistakable kinship with its namesake in physics - Heisenberg's famous Uncertainty Principle - and may indeed be regarded as providing one of mathematical interpretations for the latter. But we mention these links with Quantum Mechanics and other connections with physics and engineering only for their inspirational value, and hasten to reassure the reader that at no point in this book will he be led beyond the world of purely mathematical facts. Actually, the portion of this world charted in our book is sufficiently vast, even though we confine ourselves to trigonometric Fourier series and integrals (so that "The U. P. in Fourier Analysis" might be a slightly more appropriate title than the one we chose).
Author : J. L. Doob
Publisher : Springer Science & Business Media
ISBN 13 : 1461252083
Total Pages : 865 pages
Book Rating : 4.4/5 (612 download)
Download or read book Classical Potential Theory and Its Probabilistic Counterpart written by J. L. Doob and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 865 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Maynard Arsove
Publisher : American Mathematical Soc.
ISBN 13 : 0821822268
Total Pages : 138 pages
Book Rating : 4.8/5 (218 download)
Download or read book Algebraic Potential Theory written by Maynard Arsove and published by American Mathematical Soc.. This book was released on 1980 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Global aspects of classical and axiomatic potential theory are developed in a purely algebraic way, in terms of a new algebraic structure called a mixed lattice semigroup. This generalizes the notion of a Riesz space (vector lattice) by replacing the usual symmetrical lower and upper envelopes by unsymmetrical "mixed" lower and upper envelopes, formed relative to specific order on the first element and initial order on the second. The treatment makes essential use of a calculus of mixed envelopes, in which the main formulas and inequalities are derived through the use of certain semigroups of nonlinear operators. Techniques based on these operator semigroups are new even in the classical setting.
