Download or read book Fatou Type Theorems written by F. Di Biase and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: A basic principle governing the boundary behaviour of holomorphic func tions (and harmonic functions) is this: Under certain growth conditions, for almost every point in the boundary of the domain, these functions ad mit a boundary limit, if we approach the bounda-ry point within certain approach regions. For example, for bounded harmonic functions in the open unit disc, the natural approach regions are nontangential triangles with one vertex in the boundary point, and entirely contained in the disc [Fat06]. In fact, these natural approach regions are optimal, in the sense that convergence will fail if we approach the boundary inside larger regions, having a higher order of contact with the boundary. The first theorem of this sort is due to J. E. Littlewood [Lit27], who proved that if we replace a nontangential region with the rotates of any fixed tangential curve, then convergence fails. In 1984, A. Nagel and E. M. Stein proved that in Euclidean half spaces (and the unit disc) there are in effect regions of convergence that are not nontangential: These larger approach regions contain tangential sequences (as opposed to tangential curves). The phenomenon discovered by Nagel and Stein indicates that the boundary behaviour of ho)omor phic functions (and harmonic functions), in theorems of Fatou type, is regulated by a second principle, which predicts the existence of regions of convergence that are sequentially larger than the natural ones.

Download or read book Fatou Type Theorems written by Fausto Di Biase and published by . This book was released on 1997 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Fatou type theorem for functions associated to conformal densities on the boundary of a metric tree written by M. Coornaert and published by . This book was released on 1993 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Approach Regions and Maximal Functions in Theorems of Fatou Type written by Fausto Di Biase and published by . This book was released on 1995 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Fatou Type Theorem for Functions Associated to Conformal Densities on the Boundary of a Metric Tree written by Michel Coornaert and published by . This book was released on 1993 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Fatou s Theorem for the Harmonic Functions of Two dimensional Ornstein Uhlenbeck Processes written by Peter Des Barres March and published by Ann Arbor, Mich. : University Microfilms International. This book was released on 1983 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Fatou Theorem for a Class of Quasi linear Elliptic Partial Differential Equations written by Treven Parker Wall and published by . This book was released on 2007 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Fatou Type Theorem for a Special Non symmetric Tube Domain written by and published by . This book was released on 1969 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On the Theorems of Fatou and Stepanoff written by Sanford J. Perlman and published by . This book was released on 1972 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Geometric Harmonic Analysis III written by Dorina Mitrea and published by Springer Nature. This book was released on 2023-05-12 with total page 980 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations. Volume III is concerned with integral representation formulas for nullsolutions of elliptic PDEs, Calderón-Zygmund theory for singular integral operators, Fatou type theorems for systems of elliptic PDEs, and applications to acoustic and electromagnetic scattering. Overall, this amounts to a powerful and nuanced theory developed on uniformly rectifiable sets, which builds on the work of many predecessors.

Download or read book A Fatou Theorem for Quasiregular Functions written by Bernt K. Øksendal and published by . This book was released on 1987 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On Generalized Fatou Theorems written by Olof Svensson and published by . This book was released on 1994 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book From Bessel To Multi index Mittag leffler Functions Enumerable Families Series In Them And Convergence written by Jordanka Paneva-konovska and published by World Scientific. This book was released on 2016-08-25 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bessel and Mittag-Leffler functions are prominent within mathematical and scientific fields due to increasing interest in non-conventional models within applied mathematics. Since the analytical solutions of many differential and integral equations of arbitrary order can be written as series of special functions of fractional calculus, they are now unavoidable tools for handling various mathematical models of integer or fractional order. From Bessel to Multi-Index Mittag-Leffler Functions analyzes this through the study of enumerable families of different classes of special functions.Enumerable families are considered and the convergence of series is investigated. Providing a unified approach to the classical power series, analogues of the classical results for the power series are obtained, and the conclusion is that each of the considered series has a similar convergence behavior to a power series. Also studied are various properties of the Bessel and Mittag-Leffler functions and their generalizations, including estimations, asymptotic formulae, fractional differentiation and integration operators.

Download or read book The Real Fatou Conjecture AM 144 Volume 144 written by Jacek Graczyk and published by Princeton University Press. This book was released on 2014-09-08 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1920, Pierre Fatou expressed the conjecture that--except for special cases--all critical points of a rational map of the Riemann sphere tend to periodic orbits under iteration. This conjecture remains the main open problem in the dynamics of iterated maps. For the logistic family x- ax(1-x), it can be interpreted to mean that for a dense set of parameters "a," an attracting periodic orbit exists. The same question appears naturally in science, where the logistic family is used to construct models in physics, ecology, and economics. In this book, Jacek Graczyk and Grzegorz Swiatek provide a rigorous proof of the Real Fatou Conjecture. In spite of the apparently elementary nature of the problem, its solution requires advanced tools of complex analysis. The authors have written a self-contained and complete version of the argument, accessible to someone with no knowledge of complex dynamics and only basic familiarity with interval maps. The book will thus be useful to specialists in real dynamics as well as to graduate students.

Download or read book Extensions of Fatou Theorems in Products of Upper Half spaces written by Olof Svensson and published by . This book was released on 1992 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Harmonic Functions on Trees and Buildings written by Adam Korǹyi (et al.) and published by American Mathematical Soc.. This book was released on 1997 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of the workshop "Harmonic Functions on Graphs" held at the Graduate Centre of CUNY in the autumn of 1995. The main papers present material from four minicourses given by leading experts: D. Cartwright, A. Figà-Talamanca, S. Sawyer, and T. Steger. These minicrouses are introductions which gradually progress to deeper and less known branches of the subject. One of the topics treated is buildings, which are discrete analogues of symmetric spaces of arbitrary rank; buildings of rank are trees. Harmonic analysis on buildings is a fairly new and important field of research. One of the minicourses discusses buildings from the combinatorial perspective and another examines them from the p-adic perspective. the third minicourse deals with the connections of trees with p-adic analysis, and the fourth deals with random walks, ie., with the probabilistic side of harmonic functions on trees. The book also contains the extended abstracts of 19 of the 20 lectures given by the participants on their recent results. These abstracts, well detailed and clearly understandable, give a good cross-section of the present state of research in the field.

Download or read book Library of Congress Subject Headings written by Library of Congress and published by . This book was released on 2013 with total page 1708 pages. Available in PDF, EPUB and Kindle. Book excerpt: