The monograph is devoted to integral representations for holomorphic functions in several complex variables, such as Bochner-Martinelli, Cauchy-Fantappiè, Koppelman, multidimensional logarithmic residue etc., and their boundary properties. The applications considered are problem…
Aimed toward researchers and graduate students familiar with elements of functional analysis, linear algebra, and general topology; this book contains a general study of modulars, modular spaces, and metric modular spaces. Modulars may be thought of as generalized velocity field…
This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi-Yau varieties and string theory. With its coverage of the various perspectives of a wide area of topics such as Hodge theory, Gross-Siebert program, moduli problems, t…
This book highlights a number of recent research advances in the field of symplectic and contact geometry and topology, and related areas in low-dimensional topology. This field has experienced significant and exciting growth in the past few decades, and this volume provides an …
Reconstructing or approximating objects from seemingly incomplete information is a frequent challenge in mathematics, science, and engineering. A multitude of tools designed to recover hidden information are based on Shannon's classical sampling theorem, a central pillar of Samp…
This book contains a history of real and complex analysis in the nineteenth century, from the work of Lagrange and Fourier to the origins of set theory and the modern foundations of analysis. It studies the works of many contributors including Gauss, Cauchy, Riemann, and Weierst…
by Pirio, Luc, Vitório Pereira, Jorge
fromIMPA Monographs
This book takes an in-depth look at abelian relations of codimension one webs in the complex analytic setting. In its classical form, web geometry consists in the study of webs up to local diffeomorphisms. A significant part of the theory revolves around the concept of abelian r…
This volume is dedicated to the memory of Shoshichi Kobayashi, and gathers contributions from distinguished researchers working on topics close to his research areas. The book is organized into three parts, with the first part presenting an overview of Professor Shoshichi Kobaya…
Hidden Harmony--Geometric Fantasies describes the history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range …
This authoritative text presents the classical theory of functions of a single complex variable in complete mathematical and historical detail. Requiring only minimal, undergraduate-level prerequisites, it covers the fundamental areas of the subject with depth, precision, and ri…
This volume originated in talks given in Cortona at the conference "Geometric aspects of harmonic analysis" held in honor of the 70th birthday of Fulvio Ricci. It presents timely syntheses of several major fields of mathematics as well as original research articles contributed b…
This book provides valuable insights into complex analysis, dynamical systems, geometric function theory and operator theory. Intended for a broad spectrum of readers, ranging from undergraduate and graduate mathematics students to active researchers, it offers extensive coverag…
Uniform Spaces and Measures addresses the need for an accessible and comprehensive exposition of the theory of uniform measures -- a need that became more critical when uniform measures recently reemerged in new results in abstract harmonic analysis. Until now, results about uni…
This book is a collection of papers from the 9th International ISAAC Congress held in 2013 in Kraków, Poland. The papers are devoted to recent results in mathematics, focused on analysis and a wide range of its applications. These include up-to-date findings of the following top…
This book provides an introduction to the basic ideas and tools used in mathematical analysis. It is a hybrid cross between an advanced calculus and a more advanced analysis text and covers topics in both real and complex variables. Considerable space is given to developing Riem…
This monograph systematically explores the theory of rational maps between spheres in complex Euclidean spaces and its connections to other areas of mathematics. Synthesizing research from the last forty years, the author aims for accessibility by balancing abstract concepts wit…
