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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?

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Is this the relevant wiki page? – Sasha Aug 26 '12 at 14:04
This page is related with the subject but there is no link to a counter-example – Newben Aug 26 '12 at 14:09
Would 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. – David Speyer Aug 27 '12 at 19:39
On a related note, are there domains in the complex plane where the corona problem fails to hold ? – harmonicuser Aug 27 '12 at 23:40
I suggest you contact this author 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. – 1015 Apr 15 '13 at 0:21

If you're talking about the corona problem for $H^\infty$, I'm pretty sure that it's still wide open for the polydisc.

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