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Linear and Complex Analysis Problem Book 3
The 2-volume-book is an updated, reorganized and considerably enlarged version of the previous edition of the Research Problem Book in Analysis (LNM 1043), a collection familiar to many analysts, that has sparked off much research. This new edition, created in a joint effort by a large team of analysts, is, like its predecessor, a collection of unsolved problems of modern analysis designed as informally written mini-articles, each containing not only a statement of a problem but also historical and metho- dological comments, motivation, conjectures and discussion of possible connections, of plausible approaches as well as a list of references. There are now 342 of these mini- articles, almost twice as many as in the previous edition, despite the fact that a good deal of them have been solved!
Complex Analysis, Operators, and Related Topics
This volume is devoted to some topical problems and various applications of operator theory and its interplay with modern complex analysis. 30 carefully selected surveys and research papers are united by the "operator theoretic ideology" and systematic use of modern function theoretical techniques.
Analysis of Operators on Function Spaces
This book contains both expository articles and original research in the areas of function theory and operator theory. The contributions include extended versions of some of the lectures by invited speakers at the conference in honor of the memory of Serguei Shimorin at the Mittag-Leffler Institute in the summer of 2018. The book is intended for all researchers in the fields of function theory, operator theory and complex analysis in one or several variables. The expository articles reflecting the current status of several well-established and very dynamical areas of research will be accessible and useful to advanced graduate students and young researchers in pure and applied mathematics, and also to engineers and physicists using complex analysis methods in their investigations.
Potential Theory - ICPT 94
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.
The Maz'ya Anniversary Collection
This is the first volume of a collection of articles dedicated to V.G Maz'ya on the occasion of his 60th birthday. It contains surveys on his work in different fields of mathematics or on areas to which he made essential contributions. Other articles of this book have their origin in the common work with Maz'ya. V.G Maz'ya is author or co-author of more than 300 scientific works on various fields of functional analysis, function theory, numerical analysis, partial differential equations and their application. The reviews in this book show his enormous productivity and the large variety of his work. The scond volume contains most of the invited lectures of the Conference on Functional Analysis, Partial Differential Equations and Applications held in Rostock in September 1998 in honor of V.G Maz'ya. Here different problems of functional analysis, potential theory, linear and nonlinear partial differential equations, theory of function spaces and numerical analysis are treated. The authors, who are outstanding experts in these fields, present surveys as well as new results.
Classical and Modern Potential Theory and Applications
Proceedings of the NATO Advanced Research Workshop, Château de Bonas, France, July 25--31, 1993
Laminational Models for Some Spaces of Polynomials of Any Degree
The so-called 'pinched disk' model of the Mandelbrot set is due to A. Douady, J. H. Hubbard, and W. P. Thurston. It can be described in the language of geodesic laminations.
Maximal Function Methods for Sobolev Spaces
This book discusses advances in maximal function methods related to Poincaré and Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's inequalities, and partial differential equations. Capacities are needed for fine properties of Sobolev functions and characterization of Sobolev spaces with zero boundary values. The authors consider several uniform quantitative conditions that are self-improving, such as Hardy's inequalities, capacity density conditions, and reverse Hölder inequalities. They also study Muckenhoupt weight properties of distance functions and combine these with weighted norm inequalities; notions of dimension are then used to characterize density conditions and to give sufficient and necessary conditions for Hardy's inequalities. At the end of the book, the theory of weak solutions to the p p-Laplace equation and the use of maximal function techniques is this context are discussed. The book is directed to researchers and graduate students interested in applications of geometric and harmonic analysis in Sobolev spaces and partial differential equations.
