Advanced Courses Of Mathematical Analysis Vi Proceedings Of The Sixth International School

This volume contains short courses and recent papers by several specialists in different fields of Mathematical Analysis. It offers a wide perspective of the current state of research, and new trends, in areas related to Geometric Analysis, Harmonic Analysis, Complex Analysis, Functional Analysis and History of Mathematics. The contributions are presented with a remarkable expository nature and this makes the discussed topics accessible to a more general audience.

This Proceedings contains a collection of articles by front-line researchers in Mathematical Analysis, giving the reader a wide perspective of the current research in several areas like Functional Analysis, Complex Analysis and Measure Theory. The works are a fundamental source for current and future developments in these research fields. The articles and surveys have been collected as well as reference results scattered in the corresponding literature and thus, are highly useful to researchers.

Authored by a ranking authority in Gaussian harmonic analysis, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: harmonic analysis and probability. The book is intended for a very diverse audience, from graduate students all the way to researchers working in a broad spectrum of areas in analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of real analysis as well as with classical harmonic analysis, including Calderón-Zygmund theory; also some knowledge of basic orthogonal polynomials theory would be convenient. The monograph develops the main topics of classical harmonic analysis (semigroups, covering lemmas, maximal functions, Littlewood-Paley functions, spectral multipliers, fractional integrals and fractional derivatives, singular integrals) with respect to the Gaussian measure. The text provide an updated exposition, as self-contained as possible, of all the topics in Gaussian harmonic analysis that up to now are mostly scattered in research papers and sections of books; also an exhaustive bibliography for further reading. Each chapter ends with a section of notes and further results where connections between Gaussian harmonic analysis and other connected fields, points of view and alternative techniques are given. Mathematicians and researchers in several areas will find the breadth and depth of the treatment of the subject highly useful.

This volume comprises a collection of articles by leading researchers in mathematical analysis. It provides the reader with an extensive overview of new directions and advances in topics for current and future research in the field.

This volume contains recent papers by several specialists in different fields of mathematical analysis. It offers a reasonably wide perspective of the current state of research, and new trends, in areas related to measure theory, harmonic analysis, non-associative structures in functional analysis and summability in locally convex spaces. Those interested in researching any areas of mathematical analysis will find here numerous suggestions on possible topics with an important impact today. Often, the contributions are presented in an expository nature and this makes the discussed topics accessible to a more general audience. Contents:Measurability and Semi-Continuity of Multifunctions (B Cascales)Introduction to Interpolation Theory (F Cobos)Optimality of Function Spaces in Sobolev Embeddings (L Pick)Derivations and Projections on Jordan Triples: An introduction to Nonassociative Algebra, Continuous Cohomology, and Quantum Functional Analysis (B Russo)Weighted Inequalities and Extrapolation (J Duoandikoetxea)A Note on the Off-Diagonal Muckenhoupt–Wheeden Conjecture (D Cruz-Uribe, J M Martell and C Pérez)On the Interplay Between Nonlinear Partial Differential Equations and Game Theory (J D Rossi)The Radon–Nikodým Theorem for Vector Measures and Integral Representation of Operators on Banach Function Spaces (E A Sánchez Pérez)The Orlicz–Pettis Theorem for Multiplier Convergent Series (C Swartz) Readership: Graduate students in mathematics and researchers in mathematical analysis.

This volume comprises a collection of articles by leading researchers in mathematical analysis. It provides the reader with an extensive overview of the present-day research in different areas of mathematical analysis (complex variable, harmonic analysis, real analysis and functional analysis) that holds great promise for current and future developments. These review articles are highly useful for those who want to learn about these topics, as many results scattered in the literature are reflected through the many separate papers featured herein.