Multidimensional Integral Representations

Problems of Analytic Continuation

Author: Alexander M. Kytmanov,Simona G. Myslivets

Publisher: Springer

ISBN: 3319216597

Category: Mathematics

Page: 225

View: 8762

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 problems of analytic continuation of functions from the boundary of a bounded domain in C^n. In contrast to the well-known Hartogs-Bochner theorem, this book investigates functions with the one-dimensional property of holomorphic extension along complex lines, and includes the problems of receiving multidimensional boundary analogs of the Morera theorem. This book is a valuable resource for specialists in complex analysis, theoretical physics, as well as graduate and postgraduate students with an understanding of standard university courses in complex, real and functional analysis, as well as algebra and geometry.

Complex Analysis and Related Topics

Author: E. Ramirez de Arellano,M.V. Shapiro,L.M. Tovar,N.L. Vasilevski

Publisher: Birkhäuser

ISBN: 3034886985

Category: Mathematics

Page: 284

View: 5264

This volume, addressed to researchers and postgraduate students, compiles up-to-date research and expository papers on different aspects of complex analysis, including relations to operator theory and hypercomplex analysis. Subjects include the Schrödinger equation, subelliptic operators, Lie algebras and superalgebras, among others.

Polyharmonic functions

Author: Nachman Aronszajn,Thomas M. Creese,Leonard J. Lipkin

Publisher: Oxford University Press, USA


Category: Mathematics

Page: 265

View: 9941


Harmonic and Complex Analysis in Several Variables

Author: Steven G. Krantz

Publisher: Springer

ISBN: 3319632310

Category: Mathematics

Page: 424

View: 6914

Authored by a ranking authority in harmonic analysis of several complex variables, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: complex analysis and harmonic analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of complex analysis of one and several complex variables as well as with real and functional analysis. The monograph is largely self-contained and develops the harmonic analysis of several complex variables from the first principles. The text includes copious examples, explanations, an exhaustive bibliography for further reading, and figures that illustrate the geometric nature of the subject. Each chapter ends with an exercise set. Additionally, each chapter begins with a prologue, introducing the reader to the subject matter that follows; capsules presented in each section give perspective and a spirited launch to the segment; preludes help put ideas into context. Mathematicians and researchers in several applied disciplines will find the breadth and depth of the treatment of the subject highly useful.

Several Complex Variables

Proceedings of the 1981 Hangzhou Conference


Publisher: Birkhäuser

ISBN: 9780817631895

Category: Mathematics

Page: 268

View: 6715

In recent years there has been increasing interaction among various branches of mathematics. This is especially evident in the theory of several complex variables where fruitful interplays of the methods of algebraic geometry, differential geometry, and partial differential equations have led to unexpected insights and new directions of research. In China there has been a long tradition of study in complex analysis, differential geometry and differential equations as interrelated subjects due to the influence of Professors S. S. Chern and L. K. Hua. After a long period of isolation, in recent years there is a resurgence of scientific activity and a resumption of scientific exchange with other countries. The Hangzhou conference is the first international conference in several complex variables held in China. It offered a good opportunity for mathematicians from China, U.S., Germany, Japan, Canada, and France to meet and to discuss their work. The papers presented in the conference encompass all major aspects of several complex variables, in particular, in such areas as complex differential geometry, integral representation, boundary behavior of holomorphic functions, invariant metrics, holomorphic vector bundles, and pseudoconvexity. Most of the participants wrote up their talks for these proceedings. Some of the papers are surveys and the others present original results. This volume constitutes an overview of the current trends of research in several complex variables.

The Analysis of Linear Partial Differential Operators II

Differential Operators with Constant Coefficients

Author: Lars Hörmander

Publisher: Springer Science & Business Media

ISBN: 9783540225164

Category: Mathematics

Page: 392

View: 306

Vol. II of Lars Hörmander's 4-volume treatise is mainly devoted to operators with constant coefficients. From the reviews: "...these volumes are excellently written and make for greatly profitable reading. For years to come they will surely be a main reference for anyone wishing to study partial differential operators." Mathematical Reviews

Continuous Nowhere Differentiable Functions

The Monsters of Analysis

Author: Marek Jarnicki,Peter Pflug

Publisher: Springer

ISBN: 3319126709

Category: Mathematics

Page: 299

View: 1465

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.