most recent 30 from http://mathoverflow.net 2013-06-19T00:53:45Z http://mathoverflow.net/feeds/question/54647 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/54647/reference-for-complex-analysis-jargon Hadi 2011-02-07T15:29:48Z 2012-08-04T10:47:48Z

<p>I am not a (complex) analyst but it seems that some of the questions I am working on are related to the following concepts: </p> <ol> <li>logarithmic capacity </li> <li>transfinite diameter </li> <li>Green's function of a compact set</li> <li>System of Fekete points</li> <li>upper regularization</li> </ol> <p>I have looked at various books but some of them are very old (e.g., Hille's <em>Analytic function theory</em> which was published in 1962), and most of them just explain the subject briefly. I am looking for references which are more on the advanced side rather than elementary, to be able to find in them the results I need.</p> <p>Any suggestions?</p>

http://mathoverflow.net/questions/54647/reference-for-complex-analysis-jargon/54649#54649 Charles Matthews 2011-02-07T15:43:26Z 2011-12-02T01:34:15Z

<p><a href="http://www.encyclopediaofmath.org/index.php?title=Conformal_radius_of_a_domain" rel="nofollow">Conformal radius of a domain</a> and <a href="http://www.encyclopediaofmath.org/index.php?title=Transfinite_diameter" rel="nofollow">Transfinite diameter</a> seem to have most of these terms; see also <a href="http://en.wikipedia.org/wiki/Conformal_radius" rel="nofollow">http://en.wikipedia.org/wiki/Conformal_radius</a> .</p>

http://mathoverflow.net/questions/54647/reference-for-complex-analysis-jargon/54651#54651 Gerald Edgar 2011-02-07T15:47:38Z 2011-02-07T15:47:38Z

<p>For the first two (maybe 3): L. Ahlfors: <em>Conformal Invariants: Topics in Geometric Function Theory</em></p>

http://mathoverflow.net/questions/54647/reference-for-complex-analysis-jargon/54652#54652 Andrey Rekalo 2011-02-07T15:50:04Z 2011-02-07T15:50:04Z

<p>I would say these concepts rather belong to the field of potential theory. You will find most of the definitions and a fairly advanced treatment of the subject in <a href="http://books.google.com/books?id=0-pJz_ntKH4C&amp;printsec=frontcover&amp;dq=Logarithmic+potentials+with+external+fields&amp;hl=en&amp;ei=2hRQTcrvBIjoOeTZsBY&amp;sa=X&amp;oi=book_result&amp;ct=result&amp;resnum=1&amp;ved=0CCYQ6AEwAA#v=onepage&amp;q&amp;f=false" rel="nofollow"><em>Logarithmic Potentials with External Fields</em></a> by Saff and Totik.</p>

http://mathoverflow.net/questions/54647/reference-for-complex-analysis-jargon/56031#56031 makman 2011-02-20T02:20:51Z 2011-02-20T02:20:51Z

<p>J. B. Garnett, D. E. Marshall: <em>Harmonic Measure</em> And also Carleson's (I don't remember the name of the book) book contains at least first two.</p>

http://mathoverflow.net/questions/54647/reference-for-complex-analysis-jargon/82422#82422 Malik Younsi 2011-12-02T01:56:50Z 2011-12-02T01:56:50Z

<p>I really recommend the book <a href="http://books.google.ca/books?id=bukn-Rs-t3sC&amp;pg=PR9&amp;lpg=PR9&amp;dq=potential+theory+in+the+complex+plane&amp;source=bl&amp;ots=_kLyeM3BMt&amp;sig=7DuH0JZqkx9_qB_1NfesPslI0dY&amp;hl=en&amp;ei=wi_YTtK2IIHv0gGWyJDLDQ&amp;sa=X&amp;oi=book_result&amp;ct=result&amp;resnum=5&amp;ved=0CEMQ6AEwBA#v=onepage&amp;q&amp;f=false" rel="nofollow">Potential Theory in the complex plane" </a> by Thomas Ransford.</p> <p>It's a very nice book with exercises and it covers each of the 5 points you mentioned.</p>

http://mathoverflow.net/questions/54647/reference-for-complex-analysis-jargon/103933#103933 Alexandre Eremenko 2012-08-04T10:47:48Z 2012-08-04T10:47:48Z

<p>Goluzin, Geometric theory of functions of a complex variable, contains a very comprehensive discussion of transfinite diameter, Fekete points etc. Ransford's book mentioned above is also very nice.</p>