Advanced Courses Of Mathematical Analysis Iv

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.

This proceedings is 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. Contents:Mini-Courses:Weyl Type Theorems for Bounded Linear Operators on Banach Spaces (Pietro Aiena)Finitely Additive Measures in Action (Joe Diestel and Angela Spalsbury)Sampling and Recovery of Bandlimited Functions and Applications to Signal Processing (Th. Schlumprecht)Plenary Speakers:Isometric Shifts Between Spaces of Continuous Functions (Jesús Araujo)Uniform Algebras of Symmetric Holomorphic Functions (Richard M Aron and Pablo Galindo)Some Results on the Local Theory of Normed Spaces Since 2002 (1997) (F J García-Pacheco)A Survey on Linear (Additive) Preserver Problems (Mostafa Mbekhta)Bounded Approximation Properties via Banach Operator Ideals (Eve Oja)Linear or Bilinear Mappings Between Spaces of Continuous or Lipschitz Functions (Fernando Rambla-Barreno)Summability and Lineability in the Work of Antonio Aizpuru Tomás (Juan B Seoane-Sepúlveda)Optimal Bounds for the Hardy Operator Minus the Identity (Javier Soria) Readership: Researchers and professionals in analysis. Keywords:Mathematical Analysis;Functional Analysis;Complex Analysis;Measure TheoryKey Features:There are surveys on: Weyl type theorems in the theory of bounded linear operators, forward shifts between spaces of continuous functions, algebras of holomorphic functions, finitely additive measures, linear preserver problems, the contributions to Functional Analysis by Antonio Aizpuru Tomás and the "Cádiz school"Some very prominent contributors: R Aron, J Diestel, T Schlumprecht, J Araújo, M Mbekhta and many othersThe results are completely up-to-date and many of them have not appeared elsewhere yet

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.

"Advanced Calculus is intended as a text for courses that furnish the backbone of the student's undergraduate education in mathematical analysis. The goal is to rigorously present the fundamental concepts within the context of illuminating examples and stimulating exercises. This book is self-contained and starts with the creation of basic tools using the completeness axiom. The continuity, differentiability, integrability, and power series representation properties of functions of a single variable are established. The next few chapters describe the topological and metric properties of Euclidean space. These are the basis of a rigorous treatment of differential calculus (including the Implicit Function Theorem and Lagrange Multipliers) for mappings between Euclidean spaces and integration for functions of several real variables."--pub. desc.

For undergraduate courses in Advanced Calculus and Real Analysis. This text presents a unified view of calculus in which theory and practice reinforce each other. It covers the theory and applications of derivatives (mostly partial), integrals, (mostly multiple or improper), and infinite series (mostly of functions rather than of numbers), at a deeper level than is found in the standard advanced calculus books.

Advanced Topics in Mathematical Analysis is aimed at researchers, graduate students, and educators with an interest in mathematical analysis, and in mathematics more generally. The book aims to present theory, methods, and applications of the selected topics that have significant, useful relevance to contemporary research.