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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.
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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