Marek Jarnicki's Books

Extension of Holomorphic Functions

By: Marek Jarnicki,Peter Pflug

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Extension of Holomorphic Functions

By: Marek Jarnicki,Peter Pflug

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

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Page Count

501

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110809788

ISBN 13

9783110809787

Invariant Distances and Metrics in Complex Analysis

By: Marek Jarnicki,Peter Pflug

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Invariant Distances and Metrics in Complex Analysis

By: Marek Jarnicki,Peter Pflug

As in the field of "Invariant Distances and Metrics in Complex Analysis" there was and is a continuous progress this is now the second extended edition of the corresponding monograph. This comprehensive book is about the study of invariant pseudodistances (non-negative functions on pairs of points) and pseudometrics (non-negative functions on the tangent bundle) in several complex variables. It is an overview over a highly active research area at the borderline between complex analysis, functional analysis and differential geometry. New chapters are covering the Wu, Bergman and several other metrics. The book considers only domains in Cn and assumes a basic knowledge of several complex variables. It is a valuable reference work for the expert but is also accessible to readers who are knowledgeable about several complex variables. Each chapter starts with a brief summary of its contents and continues with a short introduction. It ends with an "Exercises" and a "List of problems" section that gathers all the problems from the chapter. The authors have been highly successful in giving a rigorous but readable account of the main lines of development in this area.

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Page Count

880

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110253860

ISBN 13

9783110253863

Continuous Nowhere Differentiable Functions

The Monsters of Analysis

By: Marek Jarnicki,Peter Pflug

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Continuous Nowhere Differentiable Functions

The Monsters of Analysis

By: Marek Jarnicki,Peter Pflug

This book covers the construction, analysis, and theory of continuous nowhere differentiable functions, comprehensively and accessibly. After illuminating the significance of the subject through an overview of its history, the reader is introduced to the sophisticated toolkit of ideas and tricks used to study the explicit continuous nowhere differentiable functions of Weierstrass, Takagi–van der Waerden, Bolzano, and others. Modern tools of functional analysis, measure theory, and Fourier analysis are applied to examine the generic nature of continuous nowhere differentiable functions, as well as linear structures within the (nonlinear) space of continuous nowhere differentiable functions. To round out the presentation, advanced techniques from several areas of mathematics are brought together to give a state-of-the-art analysis of Riemann’s continuous, and purportedly nowhere differentiable, function. For the reader’s benefit, claims requiring elaboration, and open problems, are clearly indicated. An appendix conveniently provides background material from analysis and number theory, and comprehensive indices of symbols, problems, and figures enhance the book’s utility as a reference work. Students and researchers of analysis will value this unique book as a self-contained guide to the subject and its methods.

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Page Count

298

Publisher

Springer

Published Date

ISBN 10

3319126709

ISBN 13

9783319126708

First Steps in Several Complex Variables

Reinhardt Domains

By: Marek Jarnicki,Peter Pflug

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First Steps in Several Complex Variables

Reinhardt Domains

By: Marek Jarnicki,Peter Pflug

This book provides a comprehensive introduction to the field of several complex variables in the setting of a very special but basic class of domains, the so-called Reinhardt domains. In this way the reader may learn much about this area without encountering too many technical difficulties. Chapter 1 describes the fundamental notions and the phenomenon of simultaneous holomorphic extension. Chapter 2 presents a fairly complete discussion of biholomorphisms of bounded (complete) Reinhardt domains in the two dimensional case. The third chapter gives a classification of Reinhardt domains of existence for the most important classes of holomorphic functions. The last chapter deals with invariant functions and gives explicit calculations of many of them on certain Reinhardt domains. Numerous exercises are included to help the readers with their understanding of the material. Further results and open problems are added which may be useful as seminar topics. The primary aim of this book is to introduce students or non-experts to some of the main research areas in several complex variables. The book provides a friendly invitation to this field as the only prerequisite is a basic knowledge of analysis.

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Page Count

376

Publisher

European Mathematical Society

Published Date

ISBN 10

3037190493

ISBN 13

9783037190494

Invariant Distances and Metrics in Complex Analysis

By: Marek Jarnicki,Peter Pflug

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Invariant Distances and Metrics in Complex Analysis

By: Marek Jarnicki,Peter Pflug

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Page Count

880

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Walter de Gruyter

Published Date

ISBN 10

3110253860

ISBN 13

9783110253863

Extension of Holomorphic Functions

By: Marek Jarnicki,Peter Pflug

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Extension of Holomorphic Functions

By: Marek Jarnicki,Peter Pflug

This second extended edition of the classic reference on the extension problem of holomorphic functions in pluricomplex analysis contains a wealth of additional material, organized under the original chapter structure, and covers in a self-contained way all new and recent developments and theorems that appeared since the publication of the first edition about twenty years ago.

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Page Count

586

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110630273

ISBN 13

9783110630275

Continuous Nowhere Differentiable Functions

The Monsters of Analysis

By: Marek Jarnicki,Peter Pflug

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Continuous Nowhere Differentiable Functions

The Monsters of Analysis

By: Marek Jarnicki,Peter Pflug

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Page Count

298

Publisher

Springer

Published Date

ISBN 10

3319126709

ISBN 13

9783319126708

Separately Analytic Functions

By: Marek Jarnicki,Peter Pflug

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Separately Analytic Functions

By: Marek Jarnicki,Peter Pflug

The story of separately holomorphic functions began about 100 years ago. During the second half of the 19th century, it became known that a separately continuous function is not necessarily continuous as a function of all variables. At the beginning of the 20th century, the study of separately holomorphic functions started due to the fundamental work of Osgood and Hartogs. This book provides the first self-contained and complete presentation of the study of separately holomorphic functions, from its beginnings to current research. Most of the results presented have never been published before in book form. The text is divided into two parts. The first part deals with separately holomorphic functions, ``without singularities''. The second part addresses the situation of existing singularities. A discussion of the classical results related to separately holomorphic functions leads to the most fundamental result, the classical cross theorem as well as various extensions and generalizations, to more complicated ``crosses''. Additionally, several applications for other classes of ``separately regular'' functions are given. A solid background in basic complex analysis is a prerequisite. To make the book self contained, all the results are collected in special introductory chapters and referred to at the beginning of each section. This book is addressed to students and researchers in several complex variables as well as mathematicians and theoretical physicists interested in this area of mathematics.

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Page Count

316

Publisher

JP Medical Ltd

Published Date

ISBN 10

3037190981

ISBN 13

9783037190982

Book's by Marek Jarnicki

Extension of Holomorphic Functions

Extension of Holomorphic Functions

Invariant Distances and Metrics in Complex Analysis

Invariant Distances and Metrics in Complex Analysis

Continuous Nowhere Differentiable Functions

Continuous Nowhere Differentiable Functions

First Steps in Several Complex Variables

First Steps in Several Complex Variables

Invariant Distances and Metrics in Complex Analysis

Invariant Distances and Metrics in Complex Analysis

Extension of Holomorphic Functions

Extension of Holomorphic Functions

Continuous Nowhere Differentiable Functions

Continuous Nowhere Differentiable Functions

Separately Analytic Functions

Separately Analytic Functions

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