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Name:Harmonic Measure~tqw~ darksiderg

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Torrent description

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Harmonic Measure
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General Information
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Type.................: Ebook
Part Size............: 3,537,974 bytes




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Post Information
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Posted by............: ~tqw~

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Release Notes
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During the past two decades several remarkable new results were discovered about
harmonic measure in the complex plane. This volume offers a careful survey of
these results and an introduction to the branch of analysis that contains them.
Many of these results, due to Bishop, Carleson, Jones, Makarov, Wolff, and
others, appear here in book form for the first time. The first four chapters
present the necessary background material on univalent functions, potential
theory, and extremal length. In addition, each chapter has numerous exercises to
further inform and instruct readers. This work is accessible to students who
have completed standard graduate courses in real and complex analysis.

Table of Contents

I Jordan domains 1
II Finitely connected domains 37
III Potential theory 73
IV Extremal distance 129
V Applications and reverse inequalities 157
VI Simply connected domains, part one 200
VII Bloch functions and quasicircles 229
VIII Simply connected domains, part two 269
IX Infinitely connected domains 315
X Rectifiability and quadratic expressions 347
App. A Hardy spaces 435
App. B Mixed boundary value problems 441
App. C The Dirichlet principle 447
App. D Hausdorff measure 456
App. E Transfinite diameter and Evans functions 466
App. F Martingales, Brownian motion, and Kakutani's theorem 470
App. G Carleman's method 480
App. H External distance in finitely connected domains 484
App. I McMillan's twist point theorem 497
App. J Bloch Martingales and the law of the iterated logarithm 503
App. K A dichotomy theorem 512
App. L Two estimates on integral means 518
App. M Calderon's theorem and chord-arc domains

Product Details

* ISBN: 0521470188
* ISBN-13: 9780521470186
* Format: Hardcover, 571pp
* Publisher: Cambridge University Press
* Pub. Date: April 2005

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