The corona problem is known to fail for the complex polydisk, for dimension greater than 2. Does anyone has an explicit example of such functions?
Explicit counter-example to corona problem
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complex-analysis
examples-counterexamples
several-complex-variables
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0Is [this](http://en.wikipedia.org/wiki/Corona_theorem) the relevant wiki page? – 2012-08-26
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0This page is related with the subject but there is no link to a counter-example – 2012-08-26
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2Would you mind spelling out exactly what the Corona problem means for you? I did a little poking around and discovered a bunch of versions (different Hardy spaces; nonzero versus bounded away from zero). I don't think I'll know the answer anyway, but it will increase the odds that someone will. – 2012-08-27
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0I suggest you [contact this author](http://people.math.gatech.edu/~bwick6/research.html) directly for corona related questions and up-to-date progress. He's not on MSE, nor on MO, as far as I know. I believe it is [still open for $H^\infty$ of the polydisk](http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1487-2.pdf). – 2013-04-15
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0On a related note, are there domains in the complex plane where the corona problem fails to hold ? – 2012-08-27