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Harmonic Function Theory

Harmonic FunctionTheorySecond EditionSheldon AxlerPaul BourdonWade Ramey26 December 2000 This copyrighted pdf file is available without charge only toindividuals who have purchased a copy ofHarmonic Function Theory ,second edition. Please do not distribute this file or its password toanyone and do not post it on the web. 2001 Springer-Verlag New York, Issues In your Adobe Acrobat software, go to the File menu, select Preferences , then General , then change the setting of SmoothText and Images to determine whether this document looks bet-ter with this setting checked or unchecked. Some users reportthat the text looks considerably better on the screen with SmoothText and Images unchecked, while other users have the oppositeexperience.

facts hint at the contrast between harmonic function theory in the plane and in higher dimensions. Another key difference arises from the close connection between holomorphic and harmonic functions in the plane—a real-valued function on Ω ⊂R2 is harmonic if and only if it is locally the real part of a holomorphic function. No comparable

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